A solver like "ode45" would be the correct choice for a problem like this. It takes a function handle as its first argument of the form y' = f(t,y). You will need to convert your equations to this form, where x1 and x2 are two of the four states in y. Your function will return y', which are the derivatives of the states, expressed in terms of the other states.
Looking at the ode45 examples is a good place to start:
