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Solve With Variation of Parameters

  1. Apr 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the particular solution to [itex]t^2 y'' - t(t + 2)y' + (t+2)y = 2t^3[/itex] given that y1 = t and y2 = tet are solutions. Also, require that t > 0

    3. The attempt at a solution

    Rewrite the original equation as [itex]y'' - ((t + 2)/t)y' + ((t+2)/t^2)y = 2t[/itex]

    So first I calculate the Wronskian: [itex]W(t,t*e^t) = t^2e^t[/itex]. Thus, I have that
    [itex]Y = -t \int \frac{t*e^t * 2t}{t^2e^t} dt + t*e^t \int \frac{2t^2}{t^2*e^t}dt = -t \int 2 dt + t*e^t \int 2*e^{-t} dt = -2t^2 - 2t[/itex], which I think is the particular solution.

    However, the answer in the back of the book has no -2t term, so where have I gone wrong?
     
  2. jcsd
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