Please provide a complete and comprehensive step$-$by$-$step solution with explanations for the next

question.

Suppose that the differential equation modeling a mechanical system is given by:

$\frac{dy(t{)}^2}{d{t}^2}+8\frac{dy(t)}{dt}+16y(t)=20u(t)$

If the input $u(t)$ is given by a step function of magnitude two $(t)$ :

$($a$)$ Solve the equation analytically to find $y(t).$

$($b$)$ Plot the response $y(t)$ over the time required for the system to reach a constant value. Use a

programming language $($ MATLAB or Python$).$ You must include the code created.