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Nonlinear ODE

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data
    Solve the following equation:

    [tex]y^2- xy + (x+1)y' = 0[/tex]

    3. The attempt at a solution
    The equation isn't exact, and it isn't homogeneous.

    I've tried a range of different substitutions, including v = y - x, v = y^2, v = y^2 - xy, none of which seem to lead down a fruitful path.

    I've tried differentiating this expression, to obtain a second-order ODE, and then eliminate either the nonlinear term, or the y' term, etc, between the two expressions, but that doesn't seem to lead anywhere fruitful either..

    Any hints? :-)
  2. jcsd
  3. Sep 16, 2010 #2
    That' a Bernoulli equation. Put it in standard form and make the usual substitution. Check out any intro DE text book for an example.
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