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Homework Help: Differential Equation - Hermite's Equation

  1. May 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the general solution of y' + 2ty = 0

    2. Relevant equations

    3. The attempt at a solution

    so I know y = [tex]\Sigma^{\infty}_{n=0} a_n t^n[/tex] and y' =[tex]\Sigma^{\infty}_{n=1} n a_n t^{n-1}[/tex]

    not sure what to do next.
  2. jcsd
  3. May 24, 2009 #2


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    Homework Helper

    http://www.sosmath.com/diffeq/series/series06/series06.html" [Broken]
    Last edited by a moderator: May 4, 2017
  4. May 24, 2009 #3
    Is that first line a typo? Should it be y'' (two primes, second derivative)? I'm guessing it is because the link shows a second order DE.

    If it is a single prime, then you could do a simple integration to get the answer, unless you have been told to use a series solution.
  5. May 24, 2009 #4
    It's y' + 2ty = 0. Makes the problem a bit easier.
  6. May 24, 2009 #5


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    Yah wait a minute, what does that equation have to do with Hermite's equation? Are you SURE it isn't a second order differential equation?
  7. May 25, 2009 #6
    Find the general solution of y' + 2ty = 0
    Do you have a prescribed method (like series?)
    If not, it is very simple
    Devide the Eq by y and you get
    y´/y = -2t
    ln(y) = -t2
    y=exp(-t2) + C
    that is the general solution
  8. May 25, 2009 #7
    It might not be (even though its in the same section). But I wanted to try and solve that before I move on to the second order version.
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