MATLAB: How to define a function

argumentcommanddefinederivativediff()differential equationsdsolvedyevaluatefunction_handleinputmatlabfunctionundefinedy

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)

Best Answer

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;
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