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