Convert the piecewise function into compact form and using Laplace transform, solve y ′′
+4y=g(t),y(0)=0,y ′
(0)=0 where g(t)= ⎩
⎨
⎧
​
0,
5
1
​
(t−5),
1,
​
0≤t<5
5≤t<10
t≥10
​