Thread: Help with simplifying a 2nd order pde

I have been given the equation:

dp/dt = 4 + 1/e*(d/de(e*dp/de))

the d's are partial derivatives

I am trying to solve for p. i am told to make the assumtion that the equations are separable and then convert the equation into a ordinary differential equation.

What i have done so far:
Set the RHS = 0 4 + 1/e*(d/de(e*dp/de)) = 0
use chain rule: 4 + 1/e*dp/de + d/de(dp/de)

is what i have done correct????????

There's a couple of things you can do here! First, assume solutions in the form

.

This gives



This then implies that leaving the ODE

.

Second, let . This reduces your PDE to

.

Then assume solutions of the form and you will get two ODEs for and .