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V'' - k*V^-1/2 = 0

I then said u = V' therefore u' = u(du/dV)

so the new equation is :

u(du/dV) = V^-1/2*k

Im a little rusty on separation of variables but I got a u in the final answer which means I have to integrate again since I need the final answer in terms of V.

The goal is to prove k is proportional to V^3/2

Am i doing this right?