2nd order homogenous in to 1st order linear systems
I need help to understand this. The book (Kreyzig) is very vague to me in this area. I have a few questions to do, but all I ask is you help me with this general case so I can understand how to do the rest of my questions, and hopefully I will be able to do them on my own. [as an aside, the book shows the case of y'=Ay, the case I'm dealing with is of 2nd order...i'm lost even though its basic]
Convert the following second-order homogeneous linear DE into ho-
mogeneous linear systems of first-order ODEs, for which determine the real general solution:
y''- (k^2)y = 0, where k is not 0.