# Lagrange Charpit

1. Aug 25, 2011

### gtfitzpatrick

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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?

2. Aug 26, 2011

### gtfitzpatrick

du/dt should be -q^2