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

The derivatives in the equation are partial derivatives

the values of p,s,e are dimensionless numbers.

I am to assume that the solution is separable and then use finite difference method to solve for p, the finite difference method is not a problem. This is where i am having problems. What will the equation be after the assumption is made and the equation is simplified.

I have attempted the question:

I equated the right hand side = 0:

4 + 1/e*d/de(e*dp/de) = 0

and made the partial derivatives total derivatives and then applied the chain rule:

4 + 1/e*dp/de + d/de(dp/de). Is this correct????????