You are going to be able to try out the first guess, to see if it is enough, well before you can go through the procedure in the text. P will be given by the problem, and P 1 and P 2 will be general. The advantage is that you avoid products of trigonometric and exponential functions. This is another, more sophisticated way of finding a particular solution y p . This allows us to simplify the result of plugging in to the equation to find the coefficients.
Integration then finds the functions.