For the following differential equation and assuming y = dy/dt = 0 at t=0 ????2???? ????????2 + 6 ???????? ???????? + 8???? = 8????

 For the following differential equation and assuming y = dy/dt = 0 at t=0 

????2???? ????????2 + 6 ???????? ???????? + 8???? = 8???? 

i. Solve the equation using Laplace transform for x = a unit step function 

ii. Confirm the initial (t=0) value of y is zero; what is the final (t tending to infinity) value of y? 

iii. Hand sketch a plot of y as a function of t. Does it resemble the plots in Q1?