Question involving the solution to a Lagrange Differential Equation

  • Thread starter jbowers9
  • Start date
  • #1
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Homework Statement



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

Let y' = P
taking d/dx and rearranging gives

dx/dP - xf'(P)/{P - f(P)} = g'(P)/(P - f(P))

a 1st order linear differential equation in standard form.

Homework Equations



When I attempt to solve by the suggested standard method, I end up with the following integral:

[tex]\int f'(P)dp/(P - f(P))[/tex]

The Attempt at a Solution


I'm at a loss as how to go about integrating it.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
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Try the substitution [itex]u(p)=p-f(p)[/itex]
 
  • #3
89
1
I did and I got

[tex]\int dP/u(P) - ln|u(P)|[/tex]
What do I do with the 1st term?
 
  • #4
gabbagabbahey
Homework Helper
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I don't think you can simplify it any further without knowing what [itex]f[/itex] is. At least your integral no longer involves [itex]f'[/itex] though.
 
  • #5
89
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P = y' ; y' = dy/dx I believe.

The following site lays it out: http://www.newcircuits.com/articles.php
under Lagrange differential equation.

I was lead to this site after setting up the Euler-Lagrange equations in r,phi,theta, and became curious as to how to solve them or what kind of solutions they have. ie exact, series. Thanks.
 

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