Problem $4$

Consider the first$-$order system described by the equation

$\backslash [$

$3\backslash$dot$\{$y$\}+2$ y$=1$

$\backslash ]$

a$.$ Simulate the system response in Simulink with the initial condition $\backslash ($ y$(0)=0\backslash ).$ Submit the response plot. You do not need to submit the Simulink diagram.

b$.$ Using Laplace transform methods, solve the differential equation to find the system response $\backslash ($ y$($t$)\backslash )$ of when the initial condition is $\backslash ($ y$(0)=0\backslash ).$

d$.$ Use MATLAB to plot the response function that you found in part b$.$ Tip: It should look the same as the Simulink response plot.$)$

Pro Tip: You can always use a Simulink simulation to check whether your closed$-$form solution to a differential equation is correct.$)$