Question $3.$ Solve the following ODEs using Laplace transforms:

$($a$)y^{}(t)+y^{}(t)+3y(t)=0$;$y(0)=2,y^{}(0)=1$

$($b$)y^{}(t)+2y^{}(t)=sint$;$y(0)=1,y^{}(0)=2$

$($c$)y^{}(t)+y^{}(t)=2t$;$y(0)=1,y^{}(0)=-1$

Question $4.$ Use MATLAB to simulate and plot the outputs of the systems in Q$3($a$),($b$)$ and $($c$).$ Com$-$

pare your analytical solutions from Q$3$ to MATLAB simulations by plotting them together with subplot

in MATLAB.

Hint: Define the $Y(s)$ and simulate the output using impulse function in MATLAB, as $Y(s)1=Y(s).$

Define $Y(s)$ using numerator$],[$denominator$]).$