Solve non-linear differential analytically

Hi,

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!

Re: Solve non-linear differential analytically

Quote:

Originally Posted by

**pdizzle0** Hi,

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!

Are you using to represent ? In other words, is J your independent variable?

Re: Solve non-linear differential analytically

No, sorry for not making that clear. J is constant. k*J essentially could be considered 1 constant in this context just for the final answer J proportional to V^3/2

The independent variable in this case is x -> differentiating with respect to space

Re: Solve non-linear differential analytically