Solving Lagrange Charpit Homework Equation

[gtfitzpatrick]

Homework Statement

Use Charpits equations to solve 4u$\frac{\partial u}{\partial x}$ = $(\frac{\partial u}{\partial x})^2$

where u=1 on the line x+2y=2

Homework Equations

The Attempt at a Solution

from the charpit equations i get
$\frac{dx}{dt}$ = 4u
$\frac{dy}{dt}$ = -1
$\frac{du}{dt}$ = 4pu-q
$\frac{dp}{dt} = -4p^2$
$\frac{dq}{dt} = -4pq$

next i have to parameterise the inital conditions
the line x+2y=2
x=s
y=$\frac{2-s}{2}$

whats the next step?

 

[gtfitzpatrick]

du/dt should be -q^2