1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    rock.freak667

    User Avatar
    Homework Helper

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

    AEM

    User Avatar

    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 :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Second order ODEs- P.Integral for e^xsinx
  1. A first order ODE (Replies: 1)

  2. Second Order ODE (Replies: 4)

Loading...