Question

using Laplace transform:
x''(t)+x(t)=H(t); x(0)=1, x'(0)=0

Answer 1

in which

H(t) = 3, 0<=t<=4
= 2t-5, t>4

Answer 2

There??

Answer 3

You can also write H(t) as :

\[H(t) = 3u(t) -3u(t-4)+ (2t-5)u(t-4)\]

May be..

Answer 4

It it is right then you can solve it further by taking u(t-4) common..