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How can I determine the order of a symbolic differential equation?

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Bill Tubbs
Bill Tubbs on 24 Jul 2020
Answered: Ayush Gupta on 10 Sep 2020
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); % differential equation
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.

Accepted Answer

Ayush Gupta
Ayush Gupta on 10 Sep 2020
There doesn’t exist a direct function to determine the order of a differential equation. However, there is a workaround, and we can use the reduceDifferentialOrder and get newvars from where we can get the last element and see the occurrence of t and this is one plus than the order of equation. Refer to the following code:
syms x(t) y(t) f(t)
eqs = [diff(x(t),t,t) == diff(f(t),t,t,t), diff(y(t),t,t,t) == diff(f(t),t,t)];
vars = [x(t), y(t)];
[newEqs, newVars, R] = reduceDifferentialOrder(eqs, vars)
l = length(newVars);
s = string(newVars(l,1));
order_of_equation = count(s, 't') -1;

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