(Solved): A linear, time-invariant Differential Equation system with the input \( x(t) \) and output \( y(t) ...

A linear, time-invariant Differential Equation system with the input \( x(t) \) and output \( y(t) \) is given below; \[ \frac{d^{2} y(t)}{d t^{2}}+3 \frac{d y(t)}{d t}+2 y(t)=(1 / 2) x(t)+\frac{d x(t)}{d t} \] Solve the impulse response \( \mathrm{h}(\mathrm{t}) \) of the system. Hence solve the zero-state response, \( \mathrm{y}_{\mathrm{zs}}(\mathrm{t}) \) using convolution integral method if the input is given as \( \mathrm{x}(\mathrm{t})=\mathrm{u}(\mathrm{t}) \)