The general solution, () satisfies the following second order differential equation + + = 3 cos 2 where , and are constants and 0. The () depend on whether 2 > 4, 2 = 4 or 2 < 4.

a. Construct TWO (2) different general solutions, () and solve the models with initial conditions (0) = 2 and (0) = 0 by using undetermined coefficient method. Plot both general solutions (), for interval of 0 5 and discuss the differences.

b. Construct ONE (1) general solution, () and solve the model with initial conditions (0) = 2 and (0) = 0 by using Laplace Transform.