Solve system of linear ODEs with variable coefficients

I'm trying to solve a system of three linear differential equations with one important caveat: one of the terms assumes one of three values depending on the state of the other variables.

G(t) switches values between and depending on, for instance, whether (X-Y) is positive or negative. Can I obtain numerical solutions to this sytem in MATLAB, without having to go through Simulink?

Answer 1

[John D'Errico]

Why not? Yes, you can. Use tools like ode45, etc. Read the documentation for ode45, and you will find examples of use. Depending on the parameters in your equations, a stiff solver may be necessary, such as ode15s or ode23s.

[Ritwik Rakshit]

Thank you. ode23 worked for my case.

[Ahmad Gad]

What if I am looking for symbolic solution? Can MATLAB manage this anyway instead of me solving them with my hands? Thanks!