subs: for function and its derivative

edit

In the following code

a=var('a')
y=function('y')
f=diff(y(x),x)+5*y(x)
f.substitute_function(y,a^2).show()

gives 5x^2+2x, where as it should have given 5a^2 since the the differentiation is with respect to x not a.

What I am looking for should look like (after the substitution) :

diff(a^2,x)+5*a^2

In Mathematica this is done by

(D[y[x],x]+5y[x])/.y->Function[x,a^2]

and this gives 5a^2

Simply set

y0(x) = a^2

in the code of my answer.

Here is the full code:

sage: a = var('a')
sage: y = function('y')
sage: f = diff(y(x), x) + 5*y(x)
sage: y0(x) = a^2
sage: f.substitute_function(y, y0)
5*a^2

Interesting. This solves my problem. Thank you. However, left me with many "behind the scene" probems :)

Why doesn't substitute_function work when I define the function y as

y=functioin('y')(x)

?

y = function('y')(x) does not define a function, but the symbolic expression y(x), More precisely, it defines the Python variable y as the symbolic expression y(x). Hence y cannot be used as an argument to substitute_function.