# Revision history [back]

### Substitute expression for function in differential equation

This is related to 8293, but a lot has changed since then, so I wonder if there is a way to achieve this now. Expanding on an example from 26114, I define a differential equation based on unevaluated functions and then want to substitute one of the functions (H) by an expression (T_s^2):

sage: var('T_s')
sage: B = function('B')(T_s)
sage: E = function('E')(T_s)
sage: H = function('H')(T_s)
sage: eq_B_TS = B == H/E
sage: eq1 = diff(eq_B_TS, T_s)
sage: eq1
diff(B(T_s), T_s) == -H(T_s)*diff(E(T_s), T_s)/E(T_s)^2 + diff(H(T_s), T_s)/E(T_s)
sage: eq1.subs(H == T_s^2)
diff(B(T_s), T_s) == -T_s^2*diff(E(T_s), T_s)/E(T_s)^2 + diff(H(T_s), T_s)/E(T_s)


I expected this output:

diff(B(T_s), T_s) == -T_s^2*diff(E(T_s), T_s)/E(T_s)^2 + 2*T_s/E(T_s)


However, the substitution was not carried out inside the differential. Is this a missing feature or a bug? Basically, I would like to be able to formulate general symbolic equations including differentials and integrals, and then insert explicit expressions for the different elements that would allow evaluation of the differentials and integrals.