When Will a Particle Reach the Force Center Under an Inverse Cubed Law?

[blarggg]

Homework Statement

At t0 = 0 a particle of mass m is released from rest at x0 = b > 0 away from a fixed origin of force that attracts the particle according to the law:
F=-k/x^3
where k >0 is a constant. At what time the particle will reach the force center x =0?

Homework Equations

I honestly tried to format the equations and stuff in here but i can't get it so its problem 3 on this pdf http://www.physics.uci.edu/~sasha/courses_files/111A/Fall10/hmw3.pdf

The Attempt at a Solution

well for U i got k/(2x^2)-k/2x₀^2)

but i have no idea how i would integrate the t equation with that in place of U, and even that doesn't make sense because then at x=x₀. potential would be zero and that can't be right

 

[betel]

If your U is the same as on the problem sheet, this is not correct.
What is the potential resulting in this force?
Try separation of variables to solve the differential equation.