3. For the inhomogeneous differential equation x ′′ + 2x ′ + 10x= 100 cos(4t),
(a) Describe a system for which this differential equation wouldbe an appropriate model.
(b) Find the general solution, x(t), to the equation.
(c) Does the general solution have the expected terms? Whatbehavior do the terms describe?
(d) Find the specific solution that fits the initial conditionsx(0) = 0 and x ′ (0) = 0.
(e) Plot the solution and discuss how you see the expectedbehaviors
