Use the Laplace transform to solve the given initialvalue pr

Use the Laplace transform to solve the given initial-value problem. y\' ? 2y = ?(t ? 4), y(0) = 0

Solution

y\'-2y=delta(t-4)

By applying Laplace transform

s Y(s)- Y(0)-2Y(s)=e^(-4s)

Given Y(0)=0

Y(s)(s-2)= e^(-4s)

Y(s)= e^(-4s)/(s-2)

By applying inverse Laplace transform

y(t)= e^(2(t-4)) U(t-4)