Solve using python. For the following differential equation:

a$.$ Solve the equation using the Laplace transform method. Then, plot the solution.

b$.$ Verify your solution by using the dominant time constant to estimate the expected time for this system to reach steady state.

c$.$ Show that the steady state value obtained is consistent with that expected from the differential equation.

$2*\frac{d^2}{d{t}^2}v+2*(\frac{(d)}{dt}v)+3*v=2*u(t),v(0)=0,\frac{(d)}{dt}v(0)=0$