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Any analytical solutions to this second order nonlinear DE?

  1. Mar 7, 2006 #1
    Are there any analytical solutions to:

    ay''+bx^2y+cxy+dy=0

    where a,b,c,d are constants and y(x)

    If so how would you go about it? Is there a website that teaches you how to solve these?
     
  2. jcsd
  3. Mar 7, 2006 #2

    HallsofIvy

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    If by "analytical solutions" you mean "closed form solutions" then, in general no. The standard method of solution for such a function is to use an infinite series.
     
  4. Mar 7, 2006 #3

    arildno

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    What you've written is a LINEAR ODE, BTW.
     
  5. Mar 12, 2006 #4

    mathwonk

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    the usual technical meaning of the word "analytic" is a function defined by a power series, and in that sense , as Halls implied, the answer is yes.
     
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