If you are going to use a program to solve it. What you need is not an analytical solution.
You should solve it numerically.
can be break into two first order differential equation
You should know the initial condition and
With Euler's method:
It means that and can be calculated from and
The time step need to be small enough to avoid accumuation of numerical error.
There are better numerical method to solve it. e.g. Runge-Kutta 4th order.
I think you are learning it right now? Right?