I am trying to solve the following equation analytically. I think the solution shouldnt be that hard but I'm really rusty on these kind of things.
V'' - k*J*V^-1/2 = 0
I have then said u = V' and therefore u' = u(du/dV)
u(du/dV) - k*J*V^-1/2 = 0
now you can use separation of variables but assuming I did it correctly you get a u in the answer and since u = V' you have to start all over.
The goal of this is to prove J proportional to V^3/2
Any help on how to do this is appreciated, got to turn this in tomorrow!