How to define a function?

I am trying to define DY, which is the derivative of Y by using the "diff" command and "matlabFunction()" in order to evaluate Y(0)=1 and DY(0)=2 by using "dsolve". I am having trouble with the "diff" command, the message "Undefined function 'diff' for input arguments of type 'function_handle'." keeps coming up. I have already tried rewriting this multiple ways. Any help would be greatly appreciated. Thank you.

DE = D2y + 4*Dy + 4*y == 0
Y = matlabFunction(y)
DY = diff(Y)
DY = matlabFunction(DY)
y = dsolve(DE, Y(0)==1,DY(0)==2)

Answer 1

[Star Strider]

Take the derivative as a symbolic object, not a function handle:

syms y(t)
Dy = diff(y,t); D2y = diff(y,t,t);
DE = D2y + 4*Dy + 4*y == 0
y = dsolve(DE, y(0)==1, Dy(0)==2)
Y = matlabFunction(y)
DY = diff(y)

You can then use matlabFunction to create an anonymous function from ‘DY’.

EDIT —

This code:

syms y(t)
Dy = diff(y,t); D2y = diff(y,t,t);
DE = D2y + 4*Dy + 4*y == 0;
y = dsolve(DE, y(0)==1, Dy(0)==2);
Y_fcn = matlabFunction(y)
DY = diff(y);
DY_fcn = matlabFunction(DY)

produces these anonymous functions:

Y_fcn = @(t)exp(t.*-2.0)+t.*exp(t.*-2.0).*4.0

DY_fcn = @(t)exp(t.*-2.0).*2.0-t.*exp(t.*-2.0).*8.0;

Answer 2

[Rik]

What are you trying to do? If you don't convert the symbolic function to an anonymous function, it works just fine.

%clear is just for education purposes, use functions to keep your workspace clean.
%Needing clear is a sign of bad programming.
clear D2y DE Dy DY sol t y Y 
syms y(t)
Dy = diff(y,t); D2y = diff(y,t,t);
DE = D2y + 4*Dy + 4*y == 0;
sol = dsolve(DE, y(0)==1, Dy(0)==2);
Y=y;%Y =matlabFunction(y);
DY = diff(Y);
%DY = matlabFunction(DY);
y = dsolve(DE, Y(0)==1,DY(0)==2);
disp(y)
disp(sol)

[Pauline Li]

I have revised the code given, what I am trying to do is evaluate Y(0)=1 and DY(0)=2 using matlabFunction. The part I have trouble with is the DY=diff(Y) and DY=matlabFunction(DY).

[Rik]

If you want to run dsolve(DE, Y(0)==1,DY(0)==2) or diff(Y), Y and DY must be symbolic functions. It is as simple as that. If that is not what you are trying to solve, you need to explain what function it is you want to solve.

Conversion to anonymous function is something you can do, but afterwards you can't differentiate it.