# Homework Help: Lagrange Differential Equation

1. Apr 7, 2010

### jbowers9

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

I'm attempting to solve the following equation:

y = xf(y') + g(y')

where y' = P

y = xf(P) + g(P)

2. Relevant equations

I can restate the equation as

dx/dP - x f'(P)/(P - f(P)) = g'(P)/(P - f(P))

which is a 1st order differential equation in standard form.

3. The attempt at a solution
When I attempt to solve I get

g(P) = $$\int f'(P)dp/(P - f(P))$$

I = $$\int g'(P)dp/(P - f(P)) e^{g(P)}$$

x = e$$^{-g(P)} (I + C)$$

where C is some constant of integration.
I'm getting bogged down with g(P). If I do u(P) = P - f(P)
I get g(p) = $$\int dP/u(P)$$ - ln|u(P)|

How do I proceed?