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Homework Help: Second order nonhomogeneous ODE

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations
    yh = e(a/2)t(Acost+Bsint)
    yp = Kcos(ωt)+Msin(ωt) [when r(x)=kcos(ωt) or ksin(ωt)]

    3. The attempt at a solution

    I got the homogeneous solution, which is e-1.5t(Acost+Bsint)
    but I am having trouble with the particular solution.

    I tried the above equation, making yp=K1cos(ωt)+M1sin(ωt)+K2cos(ωt)+M2sin(ωt)
    since there are 2 trig functions as r(t).
    I couldn't solve for the variables by plugging into the original equation because I was left with 4 variables and only 2 equations.

    EDIT: realized I wasn't consistent with my independent variable, made them all t's instead of t's and x's
    Last edited: Oct 17, 2013
  2. jcsd
  3. Oct 16, 2013 #2
    K1cos(ωx) + K2cos(ωx) = (K1 + K2)cos(ωx). Having two sin/cos functions is redundant, since they are linear combinations (in this case, they are the same function, entirely).
  4. Oct 17, 2013 #3
    Ah I get it now. I solved for the values (M1+M2) and (K1+K2) instead of the variables individually and got the right answer. Thanks!
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