Diff. Eq.

I'm at a loss about how to solve the following differential equation:

x'' = x^0.25

That is, double derivative of x equals x to the 0.25th power.

It's very frustrating because I have a feeling it's very trivial. Can anybody help, please? Thanks.

>>25
The equation is a non-linear second order ODE of the form y''(x)=f(y(x)).  This is known as the "autonomous equation"

The solution to this problem is can be found here http://eqworld.ipmnet.ru/en/solutions/ode/ode0301.pdf

Integral[(C1+2*Integral[f(y),y])^(-1/2),y]=C2+/-x

Just replace f(y) with y^(0.25).  So,

Integral[(C1+8/5*y^(5/4))^(-1/2),y]=C2+/-x

So, you're not going to be able to solve explicitly for y I don't think, but you can give it a shot.