a$)$ For a LTI system gives an output $y(t)=(e^{-2t}-e^{-3t})u(t)$

in response to an input $x(t)=e^{-2t}u(t)$

find the impulse response of the system

b$)$Find the Fourier transform of $x(t)=Sin{c}^2(t)$

$($Hint: $x(t)=y^2(t)$ then $x(j)=\frac{1}{2}y(j)**y(j),**$ means conv

c$)$ Find the total energy of the signal $x(t)=\frac{4}{(t^2+4)}$

d$)$Given $x(t)$ and $h(t)$ as below find $y(t)$

$h(t)=x(-t)$