MAT244--2019F > Quiz-1

TUT0602 Quiz1

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Vickyyy:
Question: Find the solution of the initial value problem. y' - 2y = e2t, y(0) = 2Solution:
p(t) = -2, g(t) = e2t, then μ(t) = e∫-2 dt = e-2tMultiply both sides by μ(t) and we get:
e-2ty' - 2e-2ty = e-2te2t = e0 = 1Integral both sides:e-2ty = ∫1dte-2ty = t + c, where c is constanty = e2tt + e2tcSubstitue y(0) = 2 into the equation above:
2 = 0 + cc = 2Then, we obtain the solution y = e2t(t+2)

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