Solve the differential equation y'' − y' − 2y = 9e^2t , with
initial conditions y(0) = 3, y' (0) = −2, using two different
methods. Indicate clearly which methods you are using. First
method:
Second method:
Again considering y'' + 4y' + 3y = 0:
(a) Solve the IVP y'' + 4y' + 3y = 0; y(0) = 1, y'(0) = α where
α > 0.
(b) Determine the coordinates (tm,ym) of the maximum point of
the solution as a function of α.
(c) Determine the behavior of tm and ym as α →∞.