Answer to Question #85924 in Complex Analysis for Anand

Question #85924
Using the method of Laplace transform, solve the following initial value problem:
y′′ − 3y′ + 2y =4e^(2t) ,y(0) = -3 , y'(0)=5
1
Expert's answer
2019-03-14T04:49:47-0400

Denote Y(p) Laplace transform of y. Then

p2Y(p)-py(0)-y'(0)-3(pY(p)-y(0))+2Y(p)=4/(p-2)

from which

Y(p)=-7/(p-1)+4/(p-2)+4/(p-2)2

Then

y(t)=-7et+4e2t+4te2t

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