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Non Linear ODE

  1. Sep 29, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\left(\frac{dy}{dx}\right)^2 - 4x\frac{dy}{dx} + 6y = 0[/tex]

    2. Relevant equations

    A common approach we have used for similar problems has been to let P = dy/dx

    3. The attempt at a solution

    Doing so we have:

    [tex]P^2 - 4xP +6y = 0[/tex]

    [tex]\Rightarrow 6y = 4P(x - P)[/tex]

    Differentiating gives:

    [tex]6P = 4\left[P(1 - \frac{dP}{dx}) +\frac{dP}{dx}(x - P)\right] = 0[/tex]

    Now usually we try to factor this and solve each factor as a linear 1st order EQ in P. However, I am having trouble seeing a nice way to factor this, that makes each factor linear. All I can get to is

    [tex]-2\left[P+2\frac{dP}{dx} - 2x\frac{dP}{dx} + 2P\frac{dP}{dx}\right] = 0[/tex]

    Any thoughts on what to do with the bracketed term to get 2 linear EQs out of the deal?

    Thanks :smile:
  2. jcsd
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