I have this DE and I do not know how to solve it. This is a problem in my review questions that my professor handed out, but we have never done a problem like this in class, so I do not know where to start. here is the problem: x'' = 4x - 5y y'' = 2x - 3 I need to solve it using eigenvalues and eigenvectors. I know how to do this for a system of first order DE's, that is easy. But I don't know what to do for a system of second order DE's. The one method I did come up with for solving it was to convert it to a system of 4 first order DE's...but then the characteristic equation is a fourth degree polynomial. I know there has got to be a better way, but I just dont know it.