Problem $2.(5$ points.$)$ Given an LTI system with input $x(t)=e^{-t}u(t)$ and impulse response $h(t)=e^{-2t}u(t).$

$($a$)$ Determine $($without using transform pairs$)$ the Fourier transforms of $x(t)$ and $h(t).$

$($b$)$ Using the convolution property, determine the Fourier transform $Y(s)$ of the output $y(t).$

$($c$)$ From the Fourier transform of $y(t)$ as obtained in part $($b$),$ determine $y(t).$