## how to dsolve for x(t) in this case?...

in the steps below, it is not fluent to do, and appear diff(1,t)

KineticEnergy := 1/2*m*diff(x(t), t)^2;
PotentialEnergy := subs(x=x(t),int((1/R^2)^2,x));
Action := KineticEnergy - PotentialEnergy;
AA := diff(Action,x(t)) - diff(diff(Action, diff(x(t),t)),t) = 0 <-------- Dsolve this
AA := eval(subs(diff(1,t)=0,diff(Action,x(t))) - Diff(subs(p=Diff(x(t),t),diff(subs(Diff(x(t),t)=p, Action), p)),t)) = 0
dsolve(AA, x(t));

Where R is constant

## how I can dsolve this differential equation...

hi...

how I can dsolve this differential equations. parameter p is unkown.

I want to gain w(x) and u(x) and psi(x) and p.

thanks

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 > with(PDEtools, casesplit, declare);
 (4)
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## how i can dsolve this differential equations........

hi...

how i can dsolve this differential equations and obtain w(x) and U(x) and phi(x) analytical or numerically?

thanks

 (1)

 (2)

 (3)

## "unable to convert to an explicit first-order syst...

hi... I have a problem with dsolve.

"unable to convert to an explicit first-order system"

thanks

## Diff. Equation with boundary...

Hey. I have the following Diff. Equation:

diffeq := diff(y(t),t,t,t,t)+10*diff(y(t),t,t)+169*y(t)=0

and I have the conditions y(0) = 0, y'(0) = 1, and y(t) -> 0 for t -> infinity

I know how to do with the first two conditions, but how do you do it with a boundary? I've read the posts made earlier on here, but I can't seem to figure it out. I've tried:

dsolve({diffeq,y(0)=0,D(y)(0)=1,D(y)(infinity)=0},y(t))

Returns nothing.

Any help would be appreciated.

## suggestion on faster solving set of nonlinear ODEs...

#first_question :how can i solve set of nonlinear ODEs,faster or using any packages ?
#second_question :what can be some boundary conditions for this type of nonlinear ODEs? how many BCs are required for this set of nonlinear ODEs? ( to use numeric solution)

 > restart:with(DEtools):with(DifferentialAlgebra):
 > eq[1]:=diff(N(r),r\$2)+2/r*diff(N(r),r)+diff(phi(r),r)/phi(r)*diff(N(r),r)-mu^2/(32*phi(r))*N(r);
 (1)
 > eq[2]:=diff(phi(r),r\$2)+2/r*diff(phi(r),r)-1/2*diff(phi(r),r)^2/phi(r)-8*diff(N(r),r)^2/(omega*(1-2*G*M/r))*phi(r);
 (2)
 > dsolve({eq[1],eq[2]});

## ACA 2017 - Differential Algebra for an extended...

by:

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra - 2017" . It was a very interesting event. This second presentation, about "Differential algebra with mathematical functions, symbolic powers and anticommutative variables", describes a project I started working in 1997 and that is at the root of Maple's dsolve and pdsolve performance with systems of equations. It is a unique approach. Not yet emulated in any other computer algebra system.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.

Differential algebra with mathematical functions,

symbolic powers and anticommutative variables

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft

Abstract:
Computer algebra implementations of Differential Algebra typically require that the systems of equations to be tackled be rational in the independent and dependent variables and their partial derivatives, and of course that , everything is commutative.

It is possible, however, to extend this computational domain and apply Differential Algebra techniques to systems of equations that involve arbitrary compositions of mathematical functions (elementary or special), fractional and symbolic powers, as well as anticommutative variables and functions. This is the subject of this presentation, with examples of the implementation of these ideas in the Maple computer algebra system and its ODE and PDE solvers.

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 Differential polynomial forms for mathematical functions (basic)
 Differential polynomial forms for compositions of mathematical functions
 Generalization to many variables
 Arbitrary functions of algebraic expressions
 Examples of the use of this extension to include mathematical functions
 Differential Algebra with anticommutative variables

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

## method = lsode doesnot work on Coupled IVP...

the Initial value problem is well defined but i could not find solution of the problem. A number of method have been used but all are useless. How to obtained graph of the all equations. Also can we find the value of R (radius) where P is zero.coupled_IVP.mw

## where did the 3 come from? dsolve question....

The solution by Maple below is correct, but non-the-less, a little strange.

```restart;
dsolve(diff(y(x),x)=3*x^2*(y(x)^2+1),y(x));
```

Gives

Ofcourse 3*constant is still constant. But it is a little strange and have no reason for it to be there.  When I solve it by hand

What could made Maple put the 3 in there? Again, solution is 100% correct, but it could be simpler.

Maple 2017.1

## problem with simple ODE...

Dear Community,

I try to solve the following very simple ODE symbolically with the ODE Analyzer assistant, yet Maple says "unble to obtain solution". :-/

If I try to slove it with dsolve, nothing happens. Is it really so difficult?

diff(p(h),h)=A/(B+C*p(h)), p(h0)=p1

A, B, C, h0 and p1 are constants. I use Maple 2016.

best egards

Andras

## How to solve and plot system differential equation...

How to solve this problem? I want to display plot of differential equation system

Thank you :)

## why dsolve solution sometimes shows as implicit wh...

Sometimes dsolve returns solution as implicit, even when not using the `implicit` option. For example

```restart;
ode:=diff(y(x),x)=(x*y(x))^(1/2):
sol:=dsolve(ode,y(x));```

Gives

Which is the same result if I had used 'implicit'.

Is there a way to tell dsolve not to do this? is it becuase it can't solve for y(x) from the above?

Maple 2017.1

## how can i draw a plot rkf45 ...

i want to draw plot Y[1] . but i cant. thank you

restart;
with(LinearAlgebra); Digits := 15; with(plots); with(Optimization);;
NewM := Matrix(5, 5, [[4119700.0000, 0., 0., 0., 0.], [0., 175900.0000, 0., 0., 0.], [0., 0., 52796., 0., 0.], [0., 0., 0., 2002900.0000, 0.], [0., 0., 0., 0., 21711.]]); NewK := Matrix(5, 5, [[18278000.0000, 0., 0., 0., 0.], [0., 8478500.0000, 0., 0., 0.], [0., 0., 3874800.0000, 0., 0.], [0., 0., 0., 494710000.0000, 0.], [0., 0., 0., 0., 7707500.0000]]); L := Vector[column](5, [400689.480747934, 36882.2103608425, 24223.1756570268, 7197.48654698287, 5007.64668721342]); V := Vector[column](5, [4.43679672962542, 48.2014976972537, 73.3916065733549, 246.999805581163, 355.012621460930]);
Phi := Matrix(5, 5, [[1., 1., 1., 1., 1.], [1.96506022575420, 1.62041320563413, 1.42204109823483, 0.548765310483432e-1, -.795724394004826], [9.21473910149806, 2.36597630710861, -.837387679777313, -8.23805381555997, 0.930594200639915e-1], [10.5672146719479, 1.26937656539014, -.710851068914949, 12.5801876194058, -0.564138989400088e-1], [12.4282433098880, -2.02516824673162, .481291188486771, -1.71479964168293, 0.513709374343217e-2]]);
NS := ImportMatrix("D:/tabas.txt", datatype = float[8]);
t_NS := NS[() .. (), 1];
acc_NS := NS[() .. (), 2];
plot(NS, t = 0 .. 4.5, size = [800, 400]);
acc := unapply(CurveFitting:-Spline(t_NS, acc_NS/(9.81), t, degree = 1), t);
eq := seq(diff(x[i](t), t\$2)+(2*0.5e-1)*sqrt(V[i])*(diff(x[i](t), t))+V[i]*x[i](t) = L[i]*acc(t)/NewM[i, i], i = 1 .. 5, 1);
ic := [seq({x[i](0) = 0, (D(x[i]))(0) = 0}, i = 1 .. 5, 1)];
sol := seq(dsolve({eq[i], ic[i][]}, numeric, output = listprocedure), i = 1 .. 5, 1);
Z := `<,>`(seq(sol[i][2], i = 1 .. 5));
#Y := Phi . Z;
#odeplot(Y[1], t = 0 .. 10);
tabas.txt

1.mw

## how can i draw odeplot this numeric dsolve...

i want to draw plot Y[1] . but i cant. thank for you

i want to take this equation

restart;
with(LinearAlgebra); Digits := 70; with(plots);

K := Matrix(5, 5, [[18278000.0000, 0., 0., 0., 0.], [0., 8478500.0000, 0., 0., 0.], [0., 0., 3874800.0000, 0., 0.], [0., 0., 0., 494710000.0000, 0.], [0., 0., 0., 0., 7707500.0000]]); M := Matrix(5, 5, [[4119700.0000, 0., 0., 0., 0.], [0., 175900.0000, 0., 0., 0.], [0., 0., 52796., 0., 0.], [0., 0., 0., 2002900.0000, 0.], [0., 0., 0., 0., 21711.]]); L := Vector[column](5, [400689.48, 36882.21, 24223.175, 7197.4865, 5007.6466]); V := Vector[column](5, [4.4368, 48.201, 73.39160, 246.999, 355.012]);
NS := ImportMatrix("D:/tabas.txt", datatype = float[8]);
t_NS := NS[() .. (), 1];
acc_NS := NS[() .. (), 2];
plot(NS, t = 0 .. 4.5, size = [800, 400]);
acc := unapply(CurveFitting:-Spline(t_NS, acc_NS/(9.81), t, degree = 1), t);
eq := seq(diff(x[i](t), t\$2)+(2*0.5e-1)*sqrt(V[i])*(diff(x[i](t), t))+V[i]*x[i](t) = L[i]/M[i, i], i = 1 .. 5, 1);
ic := [seq({x[i](0) = 0, (D(x[i]))(0) = 0}, i = 1 .. 6, 1)];
res := evalf(seq(dsolve({eq[i], ic[i][]}, numeric, method = rkf45), i = 1 .. 5, 1));
Z := `<,>`(res[1], res[2], res[3], res[4], res[5]);
Y := Phi . Z;
#odeplot(rhs(Y[1]), t = 0 .. 4)

import file text

tabas.txt