Thread: Extended Linearity Principle

How can I solve these differential equations by using the Extended Linearity Principle.
a) Find the general solution of the differential equation
dy/dt = -4 y+ 3e^(-t)
b) Solve the initial-value problem
dy/dt +3y = cos 2t, y(0) = -1

Well, the Extended Linearity Principle says that you can solve the DE by adding together the homogeneous solution and any particular solution. So what's the homogeneous solution?