Solving 2nd order differential equation using ode45

I am trying to solve this equation

x=0.5*x''*t^2;

Initial guess

x(0)=0;%starting point
x''(0)=0;%starting acceleration

So the place my vehicle is, depends on the acceleration an the time. I want to solve this equation with ode45 so that I get the place and acc during all given times.

This is my code:

[t,x]=ode45(@fun,[0 30],[0 0])

function dX=fun(t,X)

dX(1)=X(2);
dX(2)=2*X(1)/t^2;

dX=[dX(1);dX(2)];
end

Problem is that Matlab returns only returns NaN values. Could someone please explain why?

Thanks

[Torsten]

You can't prescribe x''(0) for a second-order ODE. Only x(0) and x'(0) are allowed.

Answer 1

[madhan ravi]

Reason: Because there is division by 0 therefore nans are encountered.

[t,x]=ode45(@fun,[0.00001 30],[0.00001 0.00001])

function dX=fun(t,X)
dX(1)=X(2);
dX(2)=2*X(1)/t^2;
dX=[dX(1);dX(2)];
end