# Solving a differential equation of the form $dp/dz = (p^4 + p^3 + p^2 + p*f(z))^{(1/2)}$

I am attempting to solve a differential equation of the form

$\dfrac{dp}{dz} = (a \cdot p^4 + b \cdot p^3 + c \cdot p^2 + d \cdot p \cdot f(z))^{1/2}$

where $f(z)$ is some function only of $z$. Let us for the sake of simplicity take $f(z) = z$ as a first step, and perhaps later generalize to arbitrary $f$.

I do not know how to solve this because the DE is not separable, so I cannot just split it up and integrate. What would you suggest? Alternatively, if I had powers of $p$ to infinity, would that make the problem easier?

Any help would be much appreciated.

• These are the times I feel lucky to study numerical analysis. Feb 19 '16 at 19:57
• I would prefer to solve this analytically if possible, as the solution is a component in a much larger expression. Feb 19 '16 at 19:59
• have you tried taylor expansion? Feb 19 '16 at 20:01
• Sorry, I'm not sure what you mean. Which part of this should I Taylor expand? Feb 19 '16 at 20:03
• @cbahadir You are sending the OP to a valley of tears.
– Did
Feb 20 '16 at 9:32