finding the derivative of a functional w.r.t a function
I've defined a system as:
var('a, t'); function('x, y');
de1 = diff(x(t),t) == y(t); de2 = diff(y(t),t) == -ax(t) - (a-4)/ay(t) - y(t)^3;
I'd like to compute the derivatives of the rhs of de1 and de2 w.r.t to x(t) and y(t) (to eventually form a Jacobian matrix), i.e. the derivative of the rhs of de1 w.r.t to x(t) is Zero and w.r.t y(t) is 1. I've tried the following:
diff(de1.rhs(),y); diff(de1.rhs(),y(t)); derivative(de1.rhs(),y(t));
I get errors on all three. I'd appreciate any help. thank you.