I just came from a class lecture that tied together the relationship between linear algebra and differential equations. The lecture dealt only with homogeneous linear equations. I understood about 90% of it and want to try to tie together the loose ends. In a nutshell, if I have a homogeneous linear differential equation of degree n, where L is a linear differential operator of order n. Then the general solution of the homogeneous linear differential equation is the linear combination of n linearly independent elements of ker(L). I haven't seen this applied to an example yet, so it's not entirely clear, but have I stated the relationship correctly? I guess I'll see examples tomorrow, but I'd like to go into class with a crystal clear picture, so I can following along with what will probably be another lightning quick lecture. Can anyone provide a simple example? Thanks.