(adsbygoogle = window.adsbygoogle || []).push({}); 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 = te^{t}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?

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# Homework Help: Solve With Variation of Parameters

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