Differential equation. A(d^2/dt^2)y+B/(y^2)=0

Any help is appreciated, thanks.

A d2y/dt2 = -B/y^2
d2y/dt2 = -B/Ay^2

Multiply both sides by 2dy/dt

2(dy/dt)(d2y/dt2) = -2B (dy/dt) /Ay^2

Integrate both sides with respect to t:

(dy/dt)^2 = 2B/Ay
dy/dt = sqrt(2B/A) / sqrt(y)

sqrt(y) dy = sqrt(2B/A) dt

Integrate both sides again...

(2/3) y^(3/2) = t sqrt(2B/A) + C

y = ( 3sqrt(2B/A) t / 2 + D )^(2/3)

This type of differential equation is one of those annoying forms that you learn right at the start of the subject, and then forget about because it almost never comes up ever again. It is one of the few non-linear equations that have a closed-form solution.

Hope that helps,
Fibonacci