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Please show me a solution to the differential equation

  1. Feb 12, 2010 #1
    Can someone solve:

    y''(x) - A x^2 y = 0

    A = constant

    It is probably easy, but I took this class 23 years ago.
  2. jcsd
  3. Feb 12, 2010 #2
    This one's not so easy as far as I can tell. Fortunately others have figured it out already: http://eqworld.ipmnet.ru/en/solutions/ode/ode0202.pdf

    Here's a great website when you have an ODE that you think someone might have solved before: http://eqworld.ipmnet.ru/en/solutions/ode.htm

    I referred to the book the authors of that website have written. They have some different things written about a more general form of this equation. This book might be worth tracking down if the link above doesn't help.
    Last edited: Feb 12, 2010
  4. Feb 17, 2010 #3
    Thanks btrettel! I had a feeling that equation had an attitude.

    Now I will grind out some Bessel functions.
  5. Feb 20, 2010 #4
    Its solution is not Bessel Function. Its a Harmonic Oscillator.
    its solution must be some constant with exp(x^2).
    the differential equation for Bessel function is
    which is of course not ur differential equation.
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