High altitude balloon prediction: Second order Differential Equations

I'm trying to predict and model the trajectory (ascent, float and descent) of a high altitude balloon that does not burst. Should I use ode45? And how do I implement it with the variables that update. I have a second order differential equation that only has z" and z', along with other parameters of the balloon.

For atmospheric properties I have if statements depending on altitude.

I have intial values for altitude, velocity, volume, pressure, temp, density, and weight of gas.

RhoA is the density and is dependent upon altitude and needs to be updated every timestep.

Volume is updated: vol = vol + dVol

dVol depends on weight of the gas which depends on pressure/temp which depends on altitude.

Change in altitude will be: dz = z-old_z

After a certain amount of time I want to start decreasing the volume to start the descent of the balloon. The end goal is to graph altitude versus time and have the changing variables update every timestep for the differential equation.

[John D'Errico]

Yes. Start with ODE45. Why not try it? Read the help and examples for ODE45.

RhoA is a simple function that depends upon z, the altitude. The same applies for any other parameters. So WTP?