To make your life interesting, we'll now use the word "homogeneous" in a way that is not connected to the way we used the term when talking about first-order equations. As you'll see, second order linear homogeneous equations can be solved with a little bit of algebra (and a lot of love).

Thinking about what happens when you have complex or repeated roots for your characteristic equation.

Now we can apply some of our second order linear differential equations skills to nonhomogeneous equations. Yay!