In this exercise, we verify the Extended Linearity Principle for the nonhomogeneous equati...

In this exercise, we verify the Extended Linearity Principle for the nonhomogeneous equation

(a) Let yh(t) be a solution of the associated homogeneous equation and let yp(t) be any solution of the nonhomogeneous equation. Show that yh(t)+ yp(t) satisfies the nonhomogeneous equation by calculating d(yh + yp)/dt.

(b) Assume that yp(t) and yq(t) are solutions to the nonhomogeneous equation. Show that yp(t)− yq(t) is a solution to the associated homogeneous equation by computing d(yp – yq)/dt.