I've already coded RK4 and 4th order Adams Predictor-Corrector solvers to solve ODE systems. But what I did are for general 1st order system of ODE. I may customize them for your case or code two new functions from scratch. Anyway, as I've coded many of this kind of solvers, it's not an issue. I am the author of "Numerical Recipes for Solving Engineering Problems using MATLAB" which published in 2002.