I am trying to solve an equation dx/dt = f(x,t) where f(x,t) is a velocity. I want to solve for the positions x to obtain the trajectory x(t). I've seen that the time evolution of the positions x can be calculated using Runge-Kutta, but Matlab's implementation via ode45 (or similar) looks like it requires a function in the first argument. Here, I instead have a starting position x0 and compute the velocity at that initial point, f(x0,t0). How do I use Runge-Kutta to determine the time evolution of the position based on the velocities? If it matters, I can calculate an arbitrary instantaneous velocity f(x,t) from the forces acting on a position x. To give more context, I am calculating the velocity fxt = S*Fx where the matrix S and the force Fx both depend on the particle position, so the velocity that I calculate is a scalar.
