The undetermined-coefficient method should be used whenever possible because it is simpler. Compare it with the present method as follows.

(a) Solve y" + 4y' + 3y = 65 cos 2x by both methods, showing all details, and compare.

(b) Solve y" - 2y' + y = r₁ + r₂, r₁ = 35 x^3/2 e^xr₂ = x² by applying each method to a suitable function on the right.

(c) Experiment to invent an undetermined-coefficient method for nonhomogeneous Euler–Cauchy equations.