Consider the initial value problem 4y’’+4y’+y=0, y(0)=1, y’(0)=2.

a) Solve the initial value problem and plot the solution.

b) Determine the coordinates (tM,yM) of the maximum point.

c) Change the second initial condition toy(0)=b>0 and find the solution as a function of b.

d) Find the coordinates (tM,yM)of the maximum point in terms of b.

Describe the dependence of tM and yM on b as b increases.