Q$2.(40$ marks$)$

a$.$ Solve the following differential equation:

$4\frac{d^{2}y}{d{t}^2}+\frac{4dy}{dt}+y=sin(t)$

The initial conditions are: $y(0)=2,y^{\text{'}}()=1.(30$ marks$)$

b$.$ Find the solution of the following differential equation:

$\frac{d^{2}y}{d{t}^2}-y=e^t$

Initial conditions are: $y()=1,y^{\text{'}}()=0.(10$ marks$)$