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

restart

interface(version)

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'

# Initial conditions

ics := X(0) = 0, D(X)(0) = 1

# 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);

rkf45

Error, (in sol) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

rosenbrock

Error, (in dsolve/numeric/SC/firststep) unable to evaluate the partial derivatives of f(x,y) for stiff solution

Error, (in sol) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

gear

gear

# The solution must be this one

U := t -> t/((t*10)^2+1)

# Check ode and ics

eval(ode, X(t)=U(t));
U(0);
D(U)(0);

# 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)
);