Consider the nonhomogeneous linear equationTo find a particular solution, it is pretty cle...

Consider the nonhomogeneous linear equation

To find a particular solution, it is pretty clear that our guess must contain a cosine function, but it is not so clear that the guess must also contain a sine function.

(a) Guess yp(t) = α cos 3t and substitute this guess into the equation. Is there a value of α such that yp(t) is a solution?

(b) Write a brief paragraph explaining why the proper guess for a particular solution is yp(t) = α cos 3t + β sin 3t .