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Integral of exponential over polynomial

  1. Jan 5, 2016 #1

    AAO

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    1. The problem statement, all variables and given/known data
    Solve the ODE: y''+x*y'-y=0

    2. Relevant equations


    3. The attempt at a solution
    Since this is a variable coefficient ODE, I have used the method of reduction of order, and assumed the solution in the form: y=c1*y1+c2*y2

    In this case: y1=x, and I have the reached the integral below for the second solution (y2), Can any one tell me how to approach this integral:

    v=integral[ (x^-2) * exp (-0.5*x^2) dx]
     
    Last edited by a moderator: Jan 5, 2016
  2. jcsd
  3. Jan 5, 2016 #2

    Samy_A

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    Science Advisor
    Homework Helper

    Integration by parts leaves you with an integral that is (up to some constants) the error function.
     
    Last edited by a moderator: Jan 5, 2016
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