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Finding particular integral:

  1. Jun 20, 2010 #1
    Hi guys, this is my first post on the forums - I have a maths exam tomorrow and I'm pretty sure I will need to find the particular integral of a non-homogenous ODE. I find that pretty easy, but I'm not sure how to approach it when there are 2 different terms on the right:

    d2y/dt2 - y = 1 + 3cos(2t)

    or

    (2)d2y/dt2 - dy/dt - y = t/2 + 3e(-t)

    Any help would be much appreciated!
    Thanks

    Ben
     
  2. jcsd
  3. Jun 20, 2010 #2
    why don't you solve

    [tex] \ddot{y}-y=1 [/tex]

    [tex] \ddot{y}-y=3\cos(2t) [/tex]

    then add them together
     
  4. Jun 20, 2010 #3
    Oh ok that makes sense. It might seem silly, but I can do the second one, but I'm not sure what guess to use for the particular integral of 1?
     
  5. Jun 20, 2010 #4
    You can try powers of x for the inhomogeneous function of 1.
    [tex]Ax^2+Bx+C[/tex]

    If your exam allows, you may try the operator method. It works for all inhomogeneous function. You may refer to my tutorial in http://www.voofie.com" [Broken].

    http://www.voofie.com/content/6/introduction-to-differential-equation-and-solving-linear-differential-equations-using-operator-metho/" [Broken]
     
    Last edited by a moderator: May 4, 2017
  6. Jun 20, 2010 #5
    Cool, thanks guys!
     
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