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Homework Help: Non-homogeneous 1st order diff equation

  1. Mar 16, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi, I have to solve the following differential equation and while I can get the complimentary function I can't get the particular integral.

    y'+30y=20sin(alpha*t)+alpha*cos(alpha*t)


    2. Relevant equations

    How do I integrate the product of e^30t and alpha*cos(alpha*t) in order to find the particular integral?

    3. The attempt at a solution

    I've got y=Ce^(-30t) as the complimentary function but can get no further. Any help would be brilliant, thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 16, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    Integrate by parts

    u=e-30t

    dv=20sin(αt)+αcos(αt) dt
     
  4. Mar 16, 2010 #3
    Thanks, yeah I've been trying to do it by parts for the last little while but it get's very messy, very quickly whenever I have to integrate by parts twice. I'm rubbish at calculus, I end up with the same solution but it's obviously even near being correct.
     
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