(20 points) Use the Laplace transform to solve the given initial value problem (a,b) (a) y ′′
+4y=f(t),y(0)=0,y ′
(0)=1, where f(t)= ⎩
⎨
⎧
​
3,
5,
−2,
​
t<1,
1≤t<5,
5≤t
​