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Help on Non-Linear ODE

  1. Sep 9, 2006 #1
    Hi guys, just wondering if you can give a hand on a non-linear ODE, all you guys need to do if give me a good substituion to try...

    xy''+y'+(y')^3 = 0

    where ' = d/dx
     
  2. jcsd
  3. Sep 9, 2006 #2

    HallsofIvy

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    Do you have any reason to believe there is a "good substitution"?

    Almost all non-linear differential equations cannot be solved exactly.
     
  4. Sep 9, 2006 #3
    Because this is a problem in a text, so i believe when thye say find the exact analytical solution, they must mean one exists...
     
  5. Sep 9, 2006 #4

    HallsofIvy

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    Okay, that's a good reason! Also I just noticed that you have y' twice and no y. If you let z= y', you can reduce the order of the equation:
    xy''+y'+(y')^3 = 0 becomes xz'+ z+ z3= 0, a first order, separable equation. Solve for z and let y'= z.
     
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