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:
3. Solve the following differential equation
x^2y’’ − 2xy’ + 5y = 0.
A coil spring is suspended from the ceiling, a 16-lb weight is
attached to the end of it, and the weight then comes to rest in its
equilibrium position. The mass is in a medium that exerts a viscous
resistance of 8 lb when the mass has a velocity of 1 ft/s. It is
then pulled down 12 in. below its equilibrium position and released
with an...