Solve the following differential equation:

\[
\frac{d^{2} y(t)}{d t^{2}}+\frac{d y(t)}{d t}-2 y(t)=\frac{d x(t)}{d t}+x(t)
\]

The initial conditions are \(y\left(0^{-}ight)=2 ; \frac{d y\left(0^{-}ight)}{d t}=1\). The input is

(a) \(x(t)=\delta(t)\) an impulse

(b) \(x(t)=u(t)\) unit step

(c) \(x(t)=e^{-4 t} u(t)\) an exponential decay.