I'm writing a function that takes a differential equation in symbolic form as an argument and I want to determine the order of the equation in terms of certain variables.
Example 1 A first-order system:
syms t s y(t) u(t) R L
diff_eqn = R*y(t) + L*diff(y(t), t) == u(t);
The order (w.r.t. y(t)) is 1.
Example 2 A second-order system:
syms t s y(t) u(t) omega_n z K
diff_eqn = 1/omega_n^2*diff(y(t), t, 2) + 2*z/omega_n*diff(y(t), t) + y(t) == K*u(t);
The order is 2.
I would also like to know the order w.r.t. u(t) if possible as well which in general might not be 0.