Finding general solution of motion of forced harmonic oscillator

[Redgal]

1. The motion of a forced harmonic oscillator is determined by
d^2x/dt^2 + (w^2)x = 2cos t.
Determine the general solution in the two cases w = 2 and w is not equal to 2.

To be honest I've no idea where to start!

 

[mfb]

Can you solve the equation for a free harmonic oscillator?
d^2x/dt^2 + (w^2)x = 0

Can you guess the general shape of a solution for the forced oscillator? You can use this as ansatz for your equation, and solve it to get the coefficients.