I have a differential equation

x^2 ?x/?t = t(1+x^3)^(3/2) x(0) = 0

HOW do i solve the initial value problem for this?

I have been trying to divide the right hand side by x^2 to get the x dot (?x/?t) by itself, and then have been trying to separate it into an equality of two integrals (with ?x on one side and ?t on the other) so i can solve it, but i don't know if that is actually solving the initial value problem, or just the differential equation..

I hope this question is understandable, guess it's easy to tell how confused I am.

Thanks in advance,

Ingril