# Thread: Help with simplifying a 2nd order pde

1. ## 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????????

2. ## Re: Help with simplifying a 2nd order pde

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

$\displaystyle p = T(t) + E(e)$.

This gives

$\displaystyle T' = 4 + E'' + \frac{E'}{e}.$

This then implies that $\displaystyle T = (a+4)t + b$ leaving the ODE

$\displaystyle E'' + \frac{E'}{e} = a$.

Second, let $\displaystyle p = 4t + P$. This reduces your PDE to

$\displaystyle P_t = P_{ee} + \frac{P_e}{e}$.

Then assume solutions of the form $\displaystyle P = T(t) E(e)$ and you will get two ODEs for $\displaystyle T$ and $\displaystyle E$.