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Homework Help: Need help with differential equation of type y''+ay'+by=g(x)

  1. Apr 21, 2010 #1
    1. The problem statement, all variables and given/known data

    Is it possible to give a a value so that e^(-ax^2) becomes a solution to the differential equation y''(x)+x*y'(x)+y = 0

    2. Relevant equations

    Already given.

    3. The attempt at a solution


    I'm new to this forum and doesn't really know how the fancy Latex stuff works, but I hope you'll understand me. Anyhow, I have been sitting with this problem for a while.
    Should I take the derivative of e^(-ax^2) and put it into the equation and in that way (somehow) find out x and a?

    After the I have taken the derivative and put it into the equation I get this, which I'm fairly sure is correct :/

    4a^2*(e^(ax^2))+2a(e^(ax^2))+2a(e^(ax^2))*x+(e^(ax ^2))= 0

    What am I supposed to do next?

    I hope you understand me.

    Thanks. (nice forum btw)
  2. jcsd
  3. Apr 21, 2010 #2


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    Homework Helper

    e-ax2 ≥ 0 for all x, so you can divide throughout by it.
  4. Apr 21, 2010 #3

    Char. Limit

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    Gold Member

    If such a condition were true, then you could not divide throughout by it. However, eax2 > 0 for all x, not ≥ 0 for all x.

    So you can divide by eax2, but I wanted to correct that.
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