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## Homework Statement

A particle of mass m moves in the following (repulsive) field

U(x) = α/x², α > 0,

with α a constant parameter. Determine the (unique) trajectory of the particle, x(t), corresponding to the initial conditions of the form

x(t0) = x0 > 0,

x'(t0) = [itex]\sqrt{\frac{2}{m}(E-\frac{α}{(x0)^2})}[/itex]

## Homework Equations

^

## The Attempt at a Solution

mx''(t) = -d/dx U(x)

= - (2α/x³)

= 2α/x³

=> x''(t) = 2α/mx³

Would anyone please be able to point me on the right track to solving this stupid DE? It's really starting to mess with my mind now!

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