Multivariable Integration / Nonlinear Differentials

[MrMumbleX]

Homework Statement

dv/dt = (k+v²)/h

Homework Equations

k is a constant, and v and h are variables where h is independent of v but v is dependent of h (v is a function of h and t).

The Attempt at a Solution

dv/(k+v^2) = dt/h.
The problem I have is with dealing with the right side. I know how to integrate the left side because the left side is arctangent, but I don't know what to do with the right side.
h is independent of t, so i was thinking I can treat it as a constant here? so the right side becomes t/h?

 

[hunt_mat]

Do you know now the form of h?

 

[HallsofIvy]

h does not depend on v but v depends on h? The real question is "does h depend on t or vice-versa?" If not, then you are really saying that h is treated as a parameter.

Just treat it as a constant. You will get a family of solutions depending on the parameter h.