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Find a particular solution for a non-homogeneous differential equation

  1. May 3, 2013 #1
    Find a particular solution for the following equation:

    y"+2y'+y=12.5e-t

    I'm not sure on which method to use. Here's my attempt using the undetermined coefficients method:

    →y"+2y'+y=12.5e-t
    r2+2r+1=0
    r=-1 *not even sure if this part is useful

    →yp=e-t
    yp'=-e-t
    yp"=e-t

    →y"+2y'+y=12.5e-t
    (e-t)+2(-e-t)+(e-t)=12.5e-t

    e-t(1-2+1)=e-t(12.5)

    This is where I get stuck; I don't believe I'm taking the right approach from the get-go. Any help would be greatly appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 3, 2013 #2

    Mark44

    Staff: Mentor

    It's very useful, as it gives you the complementary solution, the solution to the homogeneous problem. Note that r = -1 is a repeated solution of the characteristic equation.
    Not a good choice for a particular solution. e-t is a solution of the homogeneous problem, so can't possibly be a solution of the nonhomogeneous problem.
     
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