# Homework Help: How to find p and q (Charpit method) for this equation

1. Apr 27, 2013

### lotusquantum

1. The problem statement, all variables and given/known data
$$2uq^2+y^2(q-p)=0$$
$$p= \partial u/\partial x$$; $$q= \partial u/\partial y$$
find the general solution

2. Relevant equations
We get the charpit equations:
$$\frac{dx}{-y^2}=\frac{dy}{4uq+y^2}=\frac{du}{-py^2+q(4uq+y^2)}=\frac{dp}{-2pq^2}=\frac{dq}{-2y(q-p)-2q^3}$$

I don't know how to find the value of p and q ??

3. The attempt at a solution
(i have tried the following ways but i cannot:
from the original equation we have: $$(q-p) =-\frac{2uq^2}{y^2}$$
substitute into the last pair equation $$\frac{dq}{-2y(-\frac{2uq^2}{y^2})-2q^3}=\frac{dp}{-2pq^2}$$
or $$\frac{dq}{dp}=\frac{1}{p}(\frac{-2u}{y}+q) => q = \frac{2u}{y}+p.c1$$
but i don't know how to find p? because any pairs will lead to a complicated equation. please experts help!! thanks )