1. ## Piecewise Laplace 1

y'' + 81y = T(t)

where T(t) =

4t from 0 to 7
28 from 7 to infinity

y(0) = 0, y'(0) = 0

Find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)

I took Laplace of both side and answer comes out to be

(1/(1-e^(-7s)))((4(1-e^(-7s)(7s+1))/s^2+(28*e^(-7s)/s)))(1/(s^2+81))

2. Originally Posted by Phyxius117
y'' + 81y = T(t)

where T(t) =

4t from 0 to 7
28 from 7 to infinity

y(0) = 0, y'(0) = 0

Find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)

I took Laplace of both side and answer comes out to be

(1/(1-e^(-7s)))((4(1-e^(-7s)(7s+1))/s^2+(28*e^(-7s)/s)))(1/(s^2+81))