Consider the differential equation ay''+by'+cy=d where d is a constant. Show that every solution of the equation approaches d/c as t goes to infinity. What happens if c=0? What if b=0?
Setting Y(t)=A, and following from that Y'(t)=0 and Y''(t)=0. I plugged these values in to the differential equation and got that A=d/c but I confused about how to find the homogenous solution and how do we know that that will go to 0 as t goes to infinity.