1. The problem statement, all variables and given/known data obtain the solution of the coupled system of equations d2X1+2X1=X2 d2X2+2X2=X1 2. Relevant equations,3. The attempt at a solution I envisioned encountering this equation using matrix methods, as outlined in this website, since it was much easier than substitution, differentiation, etc: http://tutorial.math.lamar.edu/Classes/DE/SystemsDE.aspx However, unlike the method shown in the webpage above, my equation it is a 2nd order DE. Therefore, can I follow the steps exactly as outlined in this example involving only a first order system of DE? If that is the case, then can I use the same method for the system of DE I wrote below? https://www.physicsforums.com/showthread.php?t=517819 This problem is a little bit more different, because it contains a 2nd order AND a first order DE . Thanks for the continued support!