Super-hard differential equation in classical mechanics problem

snaek
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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) = \sqrt{\frac{2}{m}(E-\frac{α}{(x0)^2})}

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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You can solve your "stupid" DE by multiplying both sides of the equation by x'. This will give you exact differentials on both sides.
 
snaek said:
=> 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!
The DE always speaks well of you.

Chestermiller said:
You can solve your "stupid" DE by multiplying both sides of the equation by x'. This will give you exact differentials on both sides.
This is a good trick to remember.
 

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