# Question:How to obtain a numerical solution of this ode?

## Question:How to obtain a numerical solution of this ode?

Maple

Hi,

Could anyone help me to numerically solve this ode?
I've tried almost all the methods Maple proposes, trying to adjust stepsizes, tolerances and so on;, always without success.

I give also the exact solution of this ode in order to compare the numerical solution to.

 > restart
 > interface(version)
 (1)
 > with(plots):
 > # Source term F := t*(-600*t/(100*t^2+1)^2+80000*t^3/(100*t^2+1)^3)/(100*t^2+1)-(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)/(1+(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)^2); plot(F, t=0..0.5);
 > # Ode ode := X(t)*diff(X(t), t\$2)-diff(X(t),t)/(1+diff(X(t),t)^2) - 'F'
 (2)
 > # Initial conditions ics := X(0) = 0, D(X)(0) = 1
 (3)
 > # I used alot methods with allways either failure or either a HFloat(undefined) printf("rkf45\n"); sol := dsolve({ode, ics}, numeric): sol(1e-8); printf("\n\nrosenbrock\n"); sol := dsolve({ode, ics}, numeric, method=rosenbrock): sol(1e-8); printf("\n\ngear\n"); sol := dsolve({ode, ics}, numeric, method=gear): sol(1e-8); printf("\n\ngear\n"); sol := dsolve({ode, ics}, numeric, method=classical[heunform]): sol(1e-8);
 gear
 gear
 (4)
 > # The solution must be this one U := t -> t/((t*10)^2+1)
 (5)
 > # Check ode and ics eval(ode, X(t)=U(t)); U(0); D(U)(0);
 (6)
 > # Plots when a solution is obtained display(   plot(U(t), t=0..1, color=blue),   odeplot(sol, [t, x(t)], t=0..1, color=red, linestyle=3) );