Understanding coupled Runga Kutta derivation

I understand Runga Kutta 4th order for use with a single ODE, but am not confident I have correctly derived how to apply RK4th to a coupled or 2nd order system. As example I have dy/dt=p; dp/dt=-4pi²y

I recognize this as SHM with w=2pi so yes, I dont need RK to solve it, but I want...



Understanding coupled Runga Kutta derivation

Understanding coupled Runga Kutta derivation