Solving Lagrange Charpit Homework Equation

[gtfitzpatrick]

Homework Statement

Use Charpits equations to solve 4u[itex]\frac{\partial u}{\partial x}[/itex] = [itex](\frac{\partial u}{\partial x})^2[/itex]

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

Homework Equations

The Attempt at a Solution

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

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

whats the next step?

 

[gtfitzpatrick]

du/dt should be -q^2