Hi Busuyi,
From my understanding, you want to know the process of solving systems of differential equations using MATLAB.
This can be done by using the dsolve function.
For example, if we have the equations -
du/dt = 3u + 4v
dv/dt = −4u + 3v
First we have to create the symbolic functions u(t) and v(t) using the syms function-
syms u(t) v(t)
Then we must define the equations using the diff function-
ode1 = diff(u) == 3*u + 4*v;
ode2 = diff(v) == -4*u + 3*v;
odes = [ode1; ode2]
Then, we pass these equations to the dsolve function to solve them-
[uSol(t),vSol(t)] = dsolve(odes)
If your equations have some constraints, then they can be specified and passed as the second argument to the dsolve function-
cond1 = u(0) == 0;
cond2 = v(0) == 1;
conds = [cond1; cond2];
[uSol(t),vSol(t)] = dsolve(odes,conds)
For more information you can refer to the following documentation-
