1) Use the Laplace transform to solve the following initial value problem: 

y″−4y′−21y=δ(t−5)

y(0)=0, y′(0)=0

Use step(t-c) for uc(t) 
y(t)=?

2) Use the Laplace transform to solve the following initial value problem:

y″+9y=8δ(t−4)

y(0)=0,y′(0)=0

Use step(t-c) for uc(t). 
y(t)=?

3) 

Use the Laplace transform to solve the following initial value problem:

y″+6y′+45y=δ(t−2)

y(0)=0,y′(0)=0

Use step(t-c) for uc(t). 
y(t)=?

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