y'' - 3y' + 2y = e(adsbygoogle = window.adsbygoogle || []).push({}); ^{t}+ t^{2}

r = 1, 2 -> y_{c}= c_{1}e^{t}+c_{2}e^{2t}

y_{p1}= Ate^{t}since Ae^{t}is a linear combination of our solution to y_{c}.

y_{p2}= At^{2}+Bt+C

y'_{p2}= 2At+B

y''_{p2}= 2A

via substitution we have

2A-3(2At+B)+2(At^{2}+Bt+C) = t^{2}

by isolating terms:

- 2At
^{2}= t^{2}

2A = 1 -> A = 1/2- -6At + 2Bt = 0

2B=3 -> B = 3/2- 2A-3B+2C = 0

1 - 9/2 + 2C = 0 -> C = -3.5/2

y_{general}= y_{c}+y_{p1}+y_{p2}

Question 1: How do I determine the A for the Ate^{t}term? same way?

Question 2: Can anyone confirm that I am doing the problem correctly, or am on the right track at all?

Thanks

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# Nonhomogeneous with constant coefficients equation

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