I feel so embarrased asking this question, but this is the place to get answers. I have a 2nd order ODE with a forcing function that needs to be manipulated and put into a matrix for a numerical method solution, ie Matlab. My question is: Is the matrix composed of a particular solution in the top row and a homogenous solution in the bottom row? Does this satisfy the requirement for two equations? Maybe I should say equation, not solution. My work: m d^2x/dt^2 + c dx/dt + kx = 0 d^2x/dt^2 = dx/dt Substituting y2 for d^2t/dx^2 and y1 for dx/dt, and realizing that y2 is the derivative of y1, I end up with, in matrix form: (I am using periods to hold the spacing) [-1/k......-c/mk]..[y2]...=[x2] [1...............-1]..[y1]...=[x1] Thank you Bill On edit, I realized I forgot the signs in the first equation. On second edit, I changed the lower equation to simplify what I was after.