Chapter 4.3, Problem 50P

Consider the equation $a{y}^{″}+b{y}^{\prime }+cy=d$, where $a,b,c$ and $d$ are constants.

(a) Find all equilibrium, or constant, solutions of this differential equation.

(b) Let $y_e$ denote an equilibrium solution, and let $Y=y-y_e$. Thus $Y$ is the deviation of a solution $y$ from an equilibrium solution. Find the differential equation satisfied by $Y$.