MATLAB: How to solve higher order multi-variable ODE systems in MATLAB

higher oder odemultivariable odenested function

I have 2 governing equations for my reactions and they are a factor of 4 different variables. How do I use a nested function to solve it.
ds/dt=(d^2s)/dx^2 – ds/dx- s
Subject to below initial & boundary conditions are
This is part of the bigger set of equations but I'm not sure how to include s, t, q and x in there. All I've worked with before has been everything in terms of changes over time, but here it's time and distance (x). s and q are concentration of two solvents. Beta, gamma and alpha are all constants.

Best Answer

The first equation is a partial differential equation. Since it is independent of q, you can solve it using MATLAB's "pdepe". After you've done this, you can use the results to get q using a solver for ordinary differential equations (e.g. ODE15S). But my guess is that you forgot to include a coupling term between the two equations (i.e. s dependent on q) which will make things more difficult.
Best wishes