Symbolic toolbox: symbolic function with a function as a "variable"

I tried to defined symbolic function with a function as a variable:

syms y(t)

syms f(t,y(t)) - but it dosn't work

and additionally

f(t,y(t))=diff(y(t))

script below is working

% LOCAL ACCURACY OF MIDPOINT METHOD
% FOR SOLVING ODE
syms f(t,z) y(t);syms h t; 
assume(diff(y(t))==f(t,y(t)))  % ODE to be solved
r(h)=y(0)-y(-h)-h*f(-h/2,y(-h)+(h/2)*f(-h,y(-h))); % error
r1=simplify(subs(diff(r,h),h,0))  % first derivative of error at t=0
r2=simplify(subs(diff(r,h,2),h,0))% second derivative of error at t=0
r3=simplify(subs(diff(r,h,3),h,0))% third derivative of error at t=0

has provided correct results (i.e. derivatives of error with respect h), but in an illegible form because the instruction "simplify" has ignored the key assumption:

assume(diff(y(t))==f(t,y(t))); 

in the case of r1 and r2, the result should be 0...

[Star Strider]

I am not certain what you want to do.

See if the compose function helps.

Answer 1

[Srivardhan Gadila]

You can define y, f & t as follows:

syms t y(t) f(t,y)

Then check for f as follows:

>> f(t,y)
 
ans =
 
f(t, y(t))

You may also refer to https://in.mathworks.com/help/symbolic/solve-a-single-differential-equation.html and related links, examples in the webpage.

[Andrzej Miekina]

Yes I found it and tried with compose

but how to assume that

f(t,y) == diff(y,t)