Answer to Question #85924 in Complex Analysis for Anand

Question

Using the method of Laplace transform, solve the following initial value problem:
y′′ − 3y′ + 2y =4e^(2t) ,y(0) = -3 , y'(0)=5

Answer 1

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)=-7e^t+4e^2t+4te^2t