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Simulating the Dynamics of a Novel Disease Outbreak...

by: Paras31 170 Maple 2024
ode dsolve numeric
December 30 2024
0  0

In this activity, we are trying to simulate an outbreak of a new infectious disease that our population of 10^6people has not been exposed to before. This means that we are starting with a single case, everyone else is susceptible to the disease, and no one is yet immune or recovered. This can for example reflect a situation where an infected person introduces a new disease into a geographically isolated population, like on an island, or even when an infections "spill over" from other animals into a human population. In terms of the initial conditions for our model, we can define: "S=10^(6) -1=999999," I = 0and R = 0. NULL

Remember, the differential equations for the simple SIR model look like this:

dS/dt = `λS`*dI/dt and `λS`*dI/dt = `λS`-I*gamma, dR/dt = I*gamma

Initial number of people in each compartment
S = 10^6-1",I=0 "and R = 0.

> 

NULL

Parameters:

gamma = .1*recovery*rate*beta and .1*recovery*rate*beta = .4*the*daily*infection*rate

> 

restart; with(plots); _local(gamma)
> 

sys := diff(s(t), t) = -lambda*s(t), diff(i(t), t) = lambda*s(t)-gamma*i(t), diff(r(t), t) = gamma*i(t)

diff(s(t), t) = -lambda*s(t), diff(i(t), t) = lambda*s(t)-gamma*i(t), diff(r(t), t) = gamma*i(t)

 (1)
> 

ic := s(0) = s__0, i(0) = i__0, r(0) = r__0
> 

gamma := .1; beta := .4; n := 10^6

.1

  

.4

  

1000000

 (2)
> 

lambda := beta*i(t)/n
> 

s__0, i__0, r__0 := 10^6-1, 1, 0
> 

NULL
> 

sols := dsolve({ic, sys}, numeric, output = listprocedure)
> 

display([odeplot(sols, [t, s(t)], 0 .. 100, color = red), odeplot(sols, [t, i(t)], 0 .. 100, color = blue), odeplot(sols, [t, r(t)], 0 .. 100, color = green)], labels = ["Time [day]", "Population"], labeldirections = [horizontal, vertical], legend = ["Susceptible", "Infected", "Recovered"], legendstyle = [location = right])

 

Remember that in a simple homogenous SIR model, `R__eff `is directly related to the proportion of the population that is susceptible:

R__eff = R__0*S/N

> 

Reff := proc (t) options operator, arrow; beta*s(t)/(gamma*n) end proc
> 

odeplot(sols, [[t, Reff(t)]], t = 0 .. 100, size = [500, 300], labels = ["Time [day]", "Reff"], labeldirections = [horizontal, vertical])

 

The effective reproduction number is highest when everyone is susceptible: at the beginning, `R__eff ` = R__0. At this point in our example, every infected cases causes an average of 4 secondary infections. Over the course of the epidemic, `R__eff ` declines in proportion to susceptibility.

The peak of the epidemic happens when `R__eff ` goes down to 1 (in the example here, after 50 days). As `R__eff `decreases further below 1, the epidemic prevalence goes into decline. This is exactly what you would expect, given your understanding of the meaning of `R__eff ` once the epidemic reaches the point where every infected case cannot cause at least one more infected case (that is, when `R__eff ` < 1), the epidemic cannot sustain itself and comes to an end.

> 

susceptible := eval(s(t), sols); infected := eval(i(t), sols); recovered := eval(r(t), sols)
> 

susceptible(51)

HFloat(219673.04834159758)

 (3)
> 

infected(51)

HFloat(401423.4112878752)

 (4)
> 

recovered(51)

HFloat(378903.54037052736)

 (5)
> 

Reffe := proc (t) options operator, arrow; beta*susceptible(t)/(gamma*n) end proc

proc (t) options operator, arrow; beta*susceptible(t)/(gamma*n) end proc

 (6)
> 

Reffe(51)

HFloat(0.8786921933663903)

 (7)

Prevalence is simply the value of Iat a given point in time. Now we can see that the incidence is the number of new cases arriving in the I compartment in a given interval of time. The way we represent this mathematically is by taking the integral of new cases over a given duration.

For example, if we wanted to calculate the incidence from day 7 to 14,

int(`&lambda;S`(t), t = 7 .. 14)

> 

lamda := proc (t) options operator, arrow; beta*infected(t)/n end proc

proc (t) options operator, arrow; beta*infected(t)/n end proc

 (8)
> 

inflow := proc (t) options operator, arrow; lamda(t)*susceptible(t) end proc

proc (t) options operator, arrow; lamda(t)*susceptible(t) end proc

 (9)
> 

int(inflow(t), t = 7 .. 14)

HFloat(78.01804723222038)

 (10)
> 

incidence_plot := plot(inflow(t), t = 0 .. 14, color = orange, labels = ["Time (days)", "Incidence Rate"], labeldirections = [horizontal, vertical], title = "Incidence Rate between t=7 and t=14")

 
> 

s, i, r := eval(s(t), sols), eval(i(t), sols), eval(r(t), sols); T := 100; dataArr := Array(-1 .. T, 1 .. 4); dataArr[-1, () .. ()] := `<,>`("Day", "Susceptible", "Infected", "Recovered")


Assign all the subsequent rows

> 

for t from 0 to T do dataArr[t, () .. ()] := `~`[round](`<,>`(t, s(t), i(t), r(t))) end do

 

Tabulate through the DocumentTools

> 

DocumentTools:-Tabulate(dataArr, alignment = left, width = 50, fillcolor = (proc (A, n, m) options operator, arrow; ifelse(n = 1, "DeepSkyBlue", "LightBlue") end proc))

Download dynamics_of_novel_disease_outbreak.mw

split screen in maple...

Asked by: Christopher2222 5860
windows gui user-interface
December 30 2024
1  6

This is probaby more of a software request and I think it would be useful. 

You can obviously open two worksheets of maple and tile them vertically to give the effect of a split screen but then all the icons of each worksheet reduce the visible on screen real estate in which you can work.

It should work similar to how Excel does it when you split cells.  It would work nicely in situations where you have a diagram or picture you are referring to during the creation of your worksheet. 

Anyways just a request, I'm sure some people would find that functionality welcome. 

Global and local in module...

Asked by: Ronan 1311
programming module global
December 30 2024
1  5

I have a global matrix with a default value set in a module. I also need the inverse of the matrix. Can the module do this?  I don't really want to have to get routines to calculate the inverse every time they are called.

restart

``

TM := module () local invMetric; export foo, bar; global Metric; Metric := Matrix(3, shape = symmetric, [[1, 0, 0], [0, 1, 0], [0, 0, 1]]); invMetric := LinearAlgebra:-MatrixInverse(rtable_eval(Metric, 'inplace')); foo := proc () print('Metric' = Metric) end proc; bar := proc () print('invMetric' = invMetric) end proc end module

_m2278573910560

 (1)

TM:-foo()

Metric = Matrix(%id = 36893490426002737860)

 (2)

TM:-bar()

invMetric = Matrix(%id = 36893490426002738460)

 (3)

Metric := Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -2})

Matrix(%id = 36893490426002715820)

 (4)

TM:-foo()

Metric = Matrix(%id = 36893490426002715820)

 (5)

TM:-bar()

invMetric = Matrix(%id = 36893490426002738460)

 (6)

NULL

Download 2024-12-30_Q_Module_Global_and_Local.mw

plotvector with legend...

Asked by: romanrieme 40
vector 3d legend
December 30 2024
1  1

Hello 

I have a 3D vector plot with 3 vectors. It would be nice to have a legend for this, but so far, I have struggled to find a solution.

At the moment, I use a caption for this, but I am not fully happy with this.legend_question.mw 

Is there a simple solution?

Thanks in advance 

How should the envelope (outer contour) of this pr...

Asked by: GFY 50
ode numeric odeplot
December 30 2024
2  4

This time domain diagram has been drawn, but if you want to draw its outer outline, how should you command it?
saopinjifen1230.mw

 

Converting a Maple Worksheet to command line .ma...

Asked by: segfault 130
convert worksheet export
December 30 2024
0  3

Is there an easy way to convert a maple worksheet to a command line .mpl file to be executed from command line?

Basically strips all the comments and just keep the commands.in the .mpl file.

The exports in the Maple interface do not produce command line executable code.

It is ok if there is a third party script also to do this.

Issue with Solving Individual Parameters in Maple...

Asked by: salim-barzani 205
type user-error
December 30 2024
0  4

When I attempt to solve for a specific parameter in Maple, it results in an error stating that the parameter does not exist. However, if I solve for all parameters, it successfully finds them, as shown in the figure. How can I resolve this issue?

parameter.mw

Round Robin with double bye...

Asked by: brian bovril 914
optimization combinatorics
December 30 2024
0  4

Hi

Following on from this question, https://www.mapleprimes.com/questions/200909-Roster-Choose-Teams
I wanted to create the sequence for n>3 teams, where n:: even and two byes.
Currently, my AI-modified code produces the wrong output, can someone modify it?

# Example usage with 8 teams and 2 byes
PrintPairings(8); 

Round 1:
  1 vs 2
  3 vs 4
  5 sits out
  8 sits out
....
:Round_Robin.mw
It should be
Round 1:
  1 vs 2
  3 vs 4
  5 vs 6
  7 sits out
  8 sits out
......
etc

Why is this type check not working?...

Asked by: Ronan 1311
type
December 29 2024
0  4

I use this type ckect elsewhere inside a package and it works. I can't get it to work in a stand alone procedure.

This was originally provided by @acer (best answer) in this question Experimental format for projective vectors - MaplePrimes

> 

restart
> 

 

> 

 

> 

test:=proc(V::{And('Vector(1)',satisfies( v->type(v[1],'Vector[:-column](3)') ) ),
               And('Vector(1)',satisfies( v->type(v[1],'Vector[:-row](3)') ) )})
print("works",V);
end proc

proc (V::{And('Vector(1)', satisfies(proc (v) options operator, arrow; type(v[1], 'Vector[:-column](3)') end proc)), And('Vector(1)', satisfies(proc (v) options operator, arrow; type(v[1], 'Vector[:-row](3)') end proc))}) print("works", V) end proc

 (1)
> 

v1:=<[<1,3,2>]>;
v2:=<[<a|b|c>]>

Vector(1, {(1) = Vector(3, {(1) = 1, (2) = 3, (3) = 2})})

  

Vector[column](%id = 36893490573309309044)

 (2)
> 

test(v1)

Error, invalid input: test expects its 1st argument, V, to be of type {And('Vector[1]',satisfies(v -> type(v[1],'Vector[:-column](3)'))), And('Vector[1]',satisfies(v -> type(v[1],'Vector[:-row](3)')))}, but received Vector(1, [Vector(3, [1,3,2])])

  
> 

test(v2)

Error, invalid input: test expects its 1st argument, V, to be of type {And('Vector[1]',satisfies(v -> type(v[1],'Vector[:-column](3)'))), And('Vector[1]',satisfies(v -> type(v[1],'Vector[:-row](3)')))}, but received Vector(1, [Vector[row](3, [a,b,c])])

  
> 

whattype(v1)

Vector[column]

 (3)
> 

whattype(v1[1])

Vector[column]

 (4)
> 

whattype(v2)

Vector[column]

 (5)
> 

whattype(v2[1])

Vector[row]

 (6)
 

 

Download 2024-12-29_Q_Type_checking_not_working.mw

A task by Ramanujan, house number wanted?...

Asked by: Alfred_F 190
number_theory
December 29 2024
2  2

A street of finite length has many houses on one side, which are numbered in consecutive order with 1, 2, 3, 4, ... Determine all house numbers where the sum of all house numbers before this house number is equal to the sum of all house numbers after it.

That's enough for this year.
I wish everyone a happy new year 2025.

relative paths does not seem to work....

Asked by: segfault 130
read linux currentdir
December 28 2024
1  4

Relative path does not seems to work on Linux.
 e.g. consider the read command
 `read  "/home/harpo/skits/slapstick/boguscalculus.mw"

At the moment I have to enter the full path above as stated to be able to read in "boguscalculus.mw"

This highly unfortunte, as generally you want to specify a path, independent of the home path.

That would mean

read "~/skits/slapstick/boguscalculus.mw"   , but this does not work. Any idea why ?

Furthermore using "currentdir" to set the current directory, I also have to use the full path from root "\" which is highly unusual.

Lastly given that I set a current directory with currentdir, how do I use the currentdir to read a file inside currentdir with read command ?

e.g.

currentdir "/home/harpo/skits"
how do I read the file in a worksheet using from the  currentdir

e.g. it should be

read "slapstick/boguscalculus.mw"

But that doesnt work either.

A new type for Maple - gtoint

by: wkehowski 20 Maple
integer type
December 28 2024
1  3

I think a new integer subtype is needed: integer greater than one, gtoint.

isgto := proc(x::anything)
  local X;
  X:=x;
  return type(X,integer) and (X>1);
end:

AddType(gtoint,z->not isgto(z));

If you get bored on New Year's Eve......

Asked by: Alfred_F 190
geometry
December 28 2024
1  8

Given 4 hummingbirds, each located at the vertex of a unit tetrahedron.
The birds begin to fly in such a way that all birds fly at the same speed and:
(1) Bird #1 always flies directly toward bird #2
(2) Bird #2 always flies directly toward bird #3
(3) Bird #3 always flies directly toward bird #4
(4) Bird #4 always flies directly toward bird #1
As one can imagine, the flying birds eventually meet and collide. (Assume the birds are very small.)

What is needed is the distance to the collision point of the hummingbirds.

Error, (in …) integer overflow detected in compile...

Asked by: sursumCorda 1174
December 28 2024
1  14

Recently, I read an old article about how to call external subroutines to speed up the evaluation tremendously. The core of that article is: 

Evidently, the Typesetting:-mrow(Typesetting:-mi( is equivalent to  when b＞0, and the `∸`(a, b) is equivalent to . 
The 𝙲 code in that article was composed separately. However, now that it is possible to generate external functions, compile and access them using a single Compiler:-Compile command, it is better to complete the entire process on the fly (in order to reduce oversights and typographical errors while coding). (Besides, the original 𝙼𝚊𝚙𝚕𝚎 implementation appears verbose and less elegant.) So I write: 

JonesM1 := Compiler:-Compile((n::posint) -> add(max(1 - max(add(ifelse(j = 0, max(j - 1, 0)!**2, irem(max(j - 1, 0)!**2, j)), j = 0 .. i) - n, 0), 0), i = 0 .. n**2), 'O' = 2): # literal translation of the above formula 

But unfortunately, I then get: 

JonesM1(1);
                               2

JonesM1(2);
                               3

JonesM1(3);
                               5

JonesM1(4);
Error, (in JonesM1) integer overflow detected in compiled code

How do I get rid of this error message? 

Note. Of course there exist a ready-to-use built-in function , but the chief aim is not to find the n-th prime number as quickly as possible; I want to see if 𝙼𝚊𝚙𝚕𝚎 can directly create a compiled version of the one-liner that implements the so-called Jones' algorithm instead of writing separate 𝙲 code like that article. (Don't confound the means with the ends.) 

Bug report: Error, (in dsolve) invalid subscript s...

Asked by: nm 10431
ode dsolve differential-equations
December 27 2024
0  2

I do not remember if I reported this before or not. Can't find it. Just in case, I am posting this.

If someone find it is duplicate, feel free to delete this. But this is in latest Maple 2024.2. May be this can be fixed in time by Maple 2025 version.

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1840 and is the same as the version installed in this computer, created 2024, December 2, 10:11 hours Pacific Time.`

> 

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

> 

ode := diff(y(x),x)/y(x)-(3*(4*x^2+y(x)^2+1))/(2*x*(4*x^2+y(x)^2-2-2*x))=0;

(diff(y(x), x))/y(x)-(3/2)*(4*x^2+y(x)^2+1)/(x*(4*x^2+y(x)^2-2-2*x)) = 0

> 

DEtools:-odeadvisor(ode);

[_rational]

> 

dsolve(ode,y(x));

Error, (in dsolve) invalid subscript selector

> 

restart;
> 

infolevel[dsolve]:=5;

5

> 

ode := diff(y(x),x)/y(x)-(3*(4*x^2+y(x)^2+1))/(2*x*(4*x^2+y(x)^2-2-2*x))=0:
> 

dsolve(ode,y(x));

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

trying inverse linear

trying homogeneous types:

trying Chini

differential order: 1; looking for linear symmetries

trying exact

Looking for potential symmetries

trying inverse_Riccati

trying an equivalence to an Abel ODE

equivalence obtained to this Abel ODE: diff(y(x),x) = 3/2*(4*x^2+1)/x/(2*x^2-x-1)*y(x)-(x^2+2*x+3)/x/(2*x^2-x-1)^2*y(x)^2+3/8*(2*x+3)/(2*x^2-x-1)^3/x*y(x)^3

trying to solve the Abel ODE ...

The relative invariant s3 is: -1/432*(8*x^4+40*x^3+45*x^2-270*x+135)/x^3/(x-1)^6/(2*x+1)^4

The first absolute invariant s5^3/s3^5 is: 729/16*(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)^3/(2*x+1)^4/(8*x^4+40*x^3+45*x^2-270*x+135)^5

The second absolute invariant s3*s7/s5^2 is: 1/3*(8*x^4+40*x^3+45*x^2-270*x+135)*(10240*x^12+133120*x^11+697600*x^10+1710080*x^9+3358592*x^8-1701568*x^7+6692592*x^6-18182448*x^5+2088072*x^4-7938000*x^3+2525985*x^2+1786050*x+2679075)/(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)^2

...checking Abel class AIL (45)

...checking Abel class AIL (310)

...checking Abel class AIR (36)

...checking Abel class AIL (301)

...checking Abel class AIL (1000)

...checking Abel class AIL (42)

...checking Abel class AIL (185)

...checking Abel class AIA (by Halphen)

...checking Abel class AIL (205)

...checking Abel class AIA (147)

...checking Abel class AIL (581)

...checking Abel class AIL (200)

...checking Abel class AIL (257)

...checking Abel class AIL (400)

...checking Abel class AIA (515)

...checking Abel class AIR (1001)

...checking Abel class AIA (201)

...checking Abel class AIA (815)

Looking for potential symmetries

... changing x -> 1/x, trying again

Looking for potential symmetries

The third absolute invariant s5*s7/s3^4 is: 243/16*(10240*x^12+133120*x^11+697600*x^10+1710080*x^9+3358592*x^8-1701568*x^7+6692592*x^6-18182448*x^5+2088072*x^4-7938000*x^3+2525985*x^2+1786050*x+2679075)/(2*x+1)^4*(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)/(8*x^4+40*x^3+45*x^2-270*x+135)^4

 ->         ======================================

 ->             ...checking Abel class D (by Appell)

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {4/27} ***

 -> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class B (by Liouville)

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {1, 4, 1/4} ***

 -> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class A (by Abel)

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -1/4} ***

 -> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class C (by Abel)

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {2, -11676447873119/75975070592769, 9/5, 15632211369872/75439744512117, 46273613050865/52325357771027, 75312059745574/25138886548531} ***

 -> Step 3: looking for a solution F depending on x

_____________________________

C = 9/5 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class AIL 1.6

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-4, 16} ***

 -> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class AIL 1.8

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -116457391291688/45108305127449, -96869842492381/35485755507516, -36964550865207/94238117721032, -32286830321303/11596568583712, 32286830321303/11596568583712, 36964550865207/94238117721032, 96869842492381/35485755507516, 116457391291688/45108305127449} ***

 -> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class AIL 1.9

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-2/9, -1/9} ***

 -> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class AIA 1.51

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -94917840318055/84247876515289, -85939756880989/51399391393709, -82210125508529/36853933366676, -74381886667083/82545981233858, -41168492684238/33804146399567, -15658703496425/19275443365317, -9175348901453/101481647952193, 3/4, 15/4, 5568553686203/113599855351490, 12774469621703/63437040534358, 17836021821409/102823494563886, 39657708622139/74009717243016, 82495450887526/27663991325651, 86656182727564/45157560524183, 90074893410229/54954593917906, 100200889070747/32282555481919, 113612565327585/103754255779069} ***

 -> Step 3: looking for a solution F depending on x

_____________________________

C = 15/4 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class AIA 1.5

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-1, 1, -113553630998996/78694251194667, -112790344818825/35834119404842, -104905620984375/18860524785743, -95409943222181/78810323073434, -77648002983645/31218435062578, -67259194033608/9576982470445, -46892223838816/86694928762723, -45901561561111/29768419326991, -34674701564566/6522678435631, 26154715634141/21099761863911, 42841215778132/81925179545457, 52638927823233/15127919203723, 54069389554571/5444364811188, 54445812264368/10328928623117, 56815569067370/40738034746481, 75614540760757/62881656939350, 76459718737483/64786816765621, 85896394925571/88677987470966, 90623073438172/24246571690325, 103628692054633/17857341616628, 117754725919014/60191028908095} ***

 -> Step 3: looking for a solution F depending on x

_____________________________

C = -1 leads to a useless solution (F does not depend on x)

_____________________________

C = -113553630998996/78694251194667 leads to a useless solution (F does not depend on x)

_____________________________

C = -112790344818825/35834119404842 leads to a useless solution (F does not depend on x)

_____________________________

C = -104905620984375/18860524785743 leads to a useless solution (F does not depend on x)

_____________________________

C = -95409943222181/78810323073434 leads to a useless solution (F does not depend on x)

_____________________________

C = -77648002983645/31218435062578 leads to a useless solution (F does not depend on x)

_____________________________

C = -67259194033608/9576982470445 leads to a useless solution (F does not depend on x)

_____________________________

C = -46892223838816/86694928762723 leads to a useless solution (F does not depend on x)

_____________________________

C = -45901561561111/29768419326991 leads to a useless solution (F does not depend on x)

_____________________________

C = -34674701564566/6522678435631 leads to a useless solution (F does not depend on x)

_____________________________

C = 26154715634141/21099761863911 leads to a useless solution (F does not depend on x)

_____________________________

C = 42841215778132/81925179545457 leads to a useless solution (F does not depend on x)

_____________________________

C = 52638927823233/15127919203723 leads to a useless solution (F does not depend on x)

_____________________________

C = 54069389554571/5444364811188 leads to a useless solution (F does not depend on x)

_____________________________

C = 54445812264368/10328928623117 leads to a useless solution (F does not depend on x)

_____________________________

C = 56815569067370/40738034746481 leads to a useless solution (F does not depend on x)

_____________________________

C = 75614540760757/62881656939350 leads to a useless solution (F does not depend on x)

_____________________________

C = 76459718737483/64786816765621 leads to a useless solution (F does not depend on x)

_____________________________

C = 85896394925571/88677987470966 leads to a useless solution (F does not depend on x)

_____________________________

C = 90623073438172/24246571690325 leads to a useless solution (F does not depend on x)

_____________________________

C = 103628692054633/17857341616628 leads to a useless solution (F does not depend on x)

_____________________________

C = 117754725919014/60191028908095 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class AIA 1.52

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-5, -4, -3, 0, 1, 2, -3/2} ***

 -> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

 ->         ======================================

 ->             ...checking Abel class AIA 1.53

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-3, -1, 1, 2, -3/2, -2/3, -1/2} ***

 -> Step 3: looking for a solution F depending on x

_____________________________

C = -3 leads to a useless solution (F does not depend on x)

_____________________________

C = -3/2 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

trying to map the Abel into a solvable 2nd order ODE

...checking Abel class AIA 2-parameter, reducible to Riccati

Error, (in dsolve) invalid subscript selector

> 

restart;
> 

ode := diff(y(x),x)/y(x)-(3*(4*x^2+y(x)^2+1))/(2*x*(4*x^2+y(x)^2-2-2*x))=0:
> 

dsolve(ode,y(x));

Error, (in dsolve) invalid subscript selector

> 

tracelast;

Error, (in dsolve) invalid subscript selector

 

 

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