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Second order ODEs- P.Integral for e^xsinx

  1. Jan 12, 2010 #1
    Hi guys, I really have no idea how to approach finding the particular integral for, say:

    f'' + 5f' + f= e^x sinx

    Could anyone help me? And for future reference how do you go about finding the PI for any combination of polynomials/exponentials/sinusoidals?

    Thanks in advance for the help!
  2. jcsd
  3. Jan 12, 2010 #2


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    Homework Helper

    The PI would just the the product of the PI for ex and sinx
  4. Jan 12, 2010 #3


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    Have you ever heard of the "Method of Undetermined Coefficients"? It is covered in introductory differential equations textbooks.

    You might try setting

    [tex] f = A e^x sin(x) + B e^x cos(x) [/tex]

    and substituting it into your DE. Then collect like terms and see what values A and B have to be in order to make the resulting expression true. ( Hint: the combination of coefficients in front of the cosine terms will have to equal zero.)
  5. Jan 17, 2010 #4
    Aha thanks for the help guys :)
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