1. The problem statement, all variables and given/known data
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(2m(E−α(x0)2))
2. Relevant equations
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3. The attempt at a solution
mx''(t) = -d/dx U(x)
= - (2α/x³)
= 2α/x³
=> x''(t) = 2α/mx³