Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I tried to solve a Blasius problem (available in maple), but I have an error. How to solve this issue.

Download Shoot_Blasius_solution.mw

What might be the reason for the GUI loosing icons during a session? It looks like this

Mouse over let the icons reappear.

This problem is not new to me and only happens from time to tim

I have not found out under what conditions this happens.
The only thing I can say is that I didn't see it after restarting Maple.
And: Only the icons on the left-most disappear.

Everything under Windows 10

Has anyone seen the same thing?

Any idea how to fix this?

I'm trying derive the equation for a matching resistor pad.  In order for me to get a solution (eg for R2), I had to "manually" solve the one equation and then substitute the resulting value in the other.  Why doesn't solve do the same thing?  

restart

NULLeq1 := (R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(1)

NULL

eq2 := R1*Rlo/(R1+Rlo)+R2 = Rhi

R1*Rlo/(R1+Rlo)+R2 = Rhi

(2)

``

R1sol := solve(eq2, R1)

-Rlo*(R2-Rhi)/(R2-Rhi+Rlo)

(3)

R2sol := solve(subs(R1 = R1sol, eq1), R2)

(Rhi^2-Rhi*Rlo)^(1/2), -(Rhi^2-Rhi*Rlo)^(1/2)

(4)

restart

NULLeq1 := (R2+Rhi)*R1/(R1+R2+Rhi) = RloNULL

(R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(5)

 

NULLeq2 := R1*Rlo/(R1+Rlo)+R2 = RhiNULL

R1*Rlo/(R1+Rlo)+R2 = Rhi

(6)

s := `assuming`([solve({eq1, eq2}, {R1, R2})], [`and`(Rhi > 0, Rlo > 0)])

{R1 = RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rlo, R2 = -(RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rhi-RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rlo-Rhi)/(RootOf((Rhi-Rlo)*_Z^2-Rhi)-1)}

(7)
 

``

Download for_help.mw

ras5_v1.mw 

How can I  change eq13 to eq14 without using op command manually?

Thank you for your help in advance,

I want to solve a big system of equations. There are 32 equations and 32 variables. Furthermaore there are a few restrictions to 8 of those variables, for example 0<t, t<1. I put the restrictions into the set of equations I want to solve. Normaly its works quite well, but today, one of the solutions was t=-2.0000000000. But this does not fit to the inequalitys I gave into the programm. Why is that? Is there a diffrence if I mark a set of inequalitys as restrictions and put them as a further property into the solve command comparded to use those inequalitys as additional equations?  

Hi,

I am the administrator of Maple in my school, and all the students use Maple in part of their exams. Is it possible  to block the access to ChatGPT thru eg. the firewall or otherwise during exams. 

The reason for this question is that the students must have access to some internet sources during exams, but definately not CharGPT.

Kind regards 

Per Kirkegaard

Hello, I try to solve the equations of the odometric model with the Maple 2024 but I have not the answers as with the hands, can you help me to verify it ?

dsolve(diff(phi(t), t) = tan(10*t)/5)

dsolve(diff(x(t), t) = V*cos(ln(1 + tan(10*t)^2)/100))

dsolve(diff(y(t), t) = V*sin(ln(1 + tan(10*t)^2)/100))

Best regards, Edern Ollivier.

I noticed that Student:-ODEs:-ODESteps does not use the newer subscripted constant of integrations for solution of odes which looks much nicer.

Is there a way to make it use same constant of integrations as dsolve() does? Compare  

This is on a worksheet using typesetting level extended. Worksheet is attached


 

restart

18836

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1724 and is the same as the version installed in this computer, created 2024, April 15, 17:29 hours Pacific Time.`

#to make Maple use the new constant of integrations. Is this still needed in Maple 2024?
dsolve(diff(y(x),x$9)=1,arbitraryconstants=subscripted):
pdsolve(diff(psi(x,t),x$9)=0,arbitraryfunctions=subscripted):

ode := diff(y(x), x$2) + 2*y(x) = 0;
Student:-ODEs:-ODESteps(ode,y(x));

ode := diff(y(x), x, x)+2*y(x) = 0

"[[,,"Let's solve"],[,,((&DifferentialD;)^2)/(&DifferentialD;x^2) y(x)+2 y(x)=0],["&bullet;",,"Highest derivative means the order of the ODE is" 2],[,,((&DifferentialD;)^2)/(&DifferentialD;x^2) y(x)],["&bullet;",,"Characteristic polynomial of ODE"],[,,r^2+2=0],["&bullet;",,"Use quadratic formula to solve for" r],[,,r=(0+/-([]))/2],["&bullet;",,"Roots of the characteristic polynomial"],[,,r=(-&ImaginaryI; sqrt(2),&ImaginaryI; sqrt(2))],["&bullet;",,"1st solution of the ODE"],[,,y[1](x)=cos(sqrt(2) x)],["&bullet;",,"2nd solution of the ODE"],[,,y[2](x)=sin(sqrt(2) x)],["&bullet;",,"General solution of the ODE"],[,,y(x)=C1 y[1](x)+C2 y[2](x)],["&bullet;",,"Substitute in solutions"],[,,y(x)=C1 cos(sqrt(2) x)+C2 sin(sqrt(2) x)]]"

#compare to this output
dsolve(ode,y(x));

y(x) = c__1*sin(2^(1/2)*x)+c__2*cos(2^(1/2)*x)


 

Download make_step_solution_use_new_constant_of_integration.mw

 

Hello Everyone;

I need to find the bifurcation point and further bifarcation diagram for the given model. But facing error. Can anybody help to do this? Can you refer some library for bifurcation analysis of ODE's? Code is attched. Thanks in Advance. 

123.mw

 

 

 

 

restart

C_m := 1.0; g_K := 36.0; I_inj := 0; g_L := .3; E_Na := 50.0; E_K := -77.0; E_L := -54.4

alpha_m := (.1*(V-25.0))/(1-exp(-(V-25.0)*(1/10))); beta_m := 4*exp(-V/(18.0)); alpha_h := 0.7e-1*exp(-V/(20.0)); beta_h := 1/(1+exp(-(V-30)*(1/10))); alpha_n := (0.1e-1*(V-10.0))/(1-exp(-(V-10.0)/(10.0))); beta_n := .125*exp(-V/(80.0)); I_Na := g_Na*m^3*h*(V-E_Na); I_K := g_K*n^4*(V-E_K); I_L := g_L*(V-E_L)

.125*exp(-0.1250000000e-1*V)

(1.1)

eq1 := (I_inj-I_Na-I_K-I_L)/C_m; m := alpha_m/(alpha_m+beta_m); n := alpha_n/(alpha_n+beta_n); h := alpha_h/(alpha_h+beta_h)

-16.32000000-1.000000000*g_Na*m^3*h*(V-50.0)-36.00000000*n^4*(V+77.0)-.3000000000*V

 

.1*(V-25.0)/((1-exp(-(1/10)*V+2.500000000))*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V)))

 

0.1e-1*(V-10.0)/((1-exp(-.1000000000*V+1.000000000))*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V)))

 

0.7e-1*exp(-0.5000000000e-1*V)/(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3)))

(1.2)

bif_eq1 := eq1 = 0;

-16.32000000-0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))-0.3600000000e-6*(V-10.0)^4*(V+77.0)/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)-.3000000000*V = 0

bif_eq2 := diff( eq1, V) = 0;

-0.2100000000e-3*g_Na*(V-25.0)^2*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.2100000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*exp(-(1/10)*V+2.500000000)/((1-exp(-(1/10)*V+2.500000000))^4*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.2100000000e-3*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*(.1/(1-exp(-(1/10)*V+2.500000000))-0.1000000000e-1*(V-25.0)*exp(-(1/10)*V+2.500000000)/(1-exp(-(1/10)*V+2.500000000))^2-.2222222222*exp(-0.5555555556e-1*V))/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^4*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.3500000000e-5*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*(-0.3500000000e-2*exp(-0.5000000000e-1*V)+(1/10)*exp(-(1/10)*V+3)/(1+exp(-(1/10)*V+3))^2)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3)))^2)-0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))-0.1440000000e-5*(V-10.0)^3*(V+77.0)/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)+0.1440000000e-6*(V-10.0)^4*(V+77.0)*exp(-.1000000000*V+1.000000000)/((1-exp(-.1000000000*V+1.000000000))^5*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)+0.1440000000e-5*(V-10.0)^4*(V+77.0)*(0.1e-1/(1-exp(-.1000000000*V+1.000000000))-0.1000000000e-2*(V-10.0)*exp(-.1000000000*V+1.000000000)/(1-exp(-.1000000000*V+1.000000000))^2-0.1562500000e-2*exp(-0.1250000000e-1*V))/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^5)-0.3600000000e-6*(V-10.0)^4/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)-.3000000000 = 0

 

 

 

bif_sol := solve({ bif_eq1,bif_eq2}, {V, g_Na});

Warning, solutions may have been lost

 

 

as the solutions, which are then expressed as the points mu, y via

   

[Back to ODE Powertool Table of Contents]

 

 

Can a plot be output to a pixel array?                                                  

Is there a way to disable Maples AI Formula Assistant? This could be relevant when using Maple for a test.

Given this simplified solution, 

sol1 := (-vin + sqrt(-4*I2^2*R^2 + vin^2))/(2*I2*omega0*L)

how do I bring the denominator back under the radical?

I have solution to system of equations that results (I assign it to) in:

I2sol := -I*omega0*k*L*vin*1/(L^2*k^2*omega0^2 + R^2)

I then try to solve it for k by doing

solve(I2sol = I2, k)

but that doesn't work.  What is the "right" Maple way to rearrange I2 such that the expression is the solution(s) for k?

I want to make the system of ODE into its dimensionless version:

Dimensional version: 

dN/dT= R*N (1 −N/K)−alpha*N*P/(A + N);

dP/dT= gamma*N*P/( A + N) + C*P/(1 + Q*P) −MP;

N (0) ≡N_0 ≥0 and P (0) ≡P_0 ≥0

R, K alpha, gamma, M, C, Q are all positive constant. 

Using one choice of dimensionless variable x = N/K , y = alpha*P/(R*K), t = R*T, the system of ODE can be reduced to its dimensionless version as follows:

dx/dt = x*(1 −x ) −x*y/(a + x);

dy/dt = b*x*y/(a + x) + c*y/(1 + q*y) −m*y

where the dimensionless parameters are a = A/K , b = gamma/R , c = C/R , q = Q*R*K/alpha, and m = M/R.

How to do this in maple. Please help. 

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