(adsbygoogle = window.adsbygoogle || []).push({}); 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) = [tex]\int f'(P)dp/(P - f(P))[/tex]

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

x = e[tex]^{-g(P)} (I + C)[/tex]

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) = [tex]\int dP/u(P)[/tex] - ln|u(P)|

How do I proceed?

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# Homework Help: Lagrange Differential Equation

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