Given a differential equation.
ie. y'' +y' + 1 =0 (THIS IS NOT THE PROBLEM THAT I AM SOLVING)
The Attempt at a Solution
The equation above is not what I'm working with, but an example of a differential equation problem that I was working on. Now, I am trying to find a homogeneous solution by guessing a value for y. However, when I make a guess for y and plug it in, the equation gives me 0 = 1. Does this mean the homogenous solution does not exist or did I not make the correct guess?