Having issues with a seemingly simple problem

[Xyius]

Homework Statement

A particle of mass m is repelled from the origin by a force inversely proportional to the cube of its distance from the origin. Set up and solve the equations of motion if the particle is initially at rest at a distance x_0 from the origin.

(This is one dimensional motion)

Homework Equations

Newtons Second Law to set up the equation of motion

The Attempt at a Solution

The first part is simple. I just had..
m \ddot{x}=\frac{k}{x^3}

And this part is right. I am having trouble solving it however. I know it is just a method from my differential equations course but I am having trouble for some reason!

 

[rude man]

Try conservation of energy - potential + kinetic.