Having issues with a seemingly simple problem

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SUMMARY

The discussion focuses on solving the equations of motion for a particle of mass m that is repelled from the origin by a force inversely proportional to the cube of its distance from the origin, described by the equation m \ddot{x} = \frac{k}{x^3}. The particle starts at rest from an initial distance x_0. Participants emphasize using Newton's Second Law and suggest applying conservation of energy principles to derive the solution, combining potential and kinetic energy concepts.

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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 [itex]x_0[/itex] 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..
[tex]m \ddot{x}=\frac{k}{x^3}[/tex]

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!
 
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Try conservation of energy - potential + kinetic.
 

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