How can I declare an implicit variable, y(t), after I have used it in a symbolically defined function?

I'm writing a scheme that solves an ODE and in doing so I declare a symbolic function:

syms t y(t)
f = t^(-2) * (sin(2*t) - 2*t*y)

At one point I have to take a total derivative, so I need to be be implicit in the expression, but I also need to evalute at a specific value of t and y. I attempt to do this in the following lines.

y(t) = wi;
out(1) = f(ti);

However, I am prompted with the following error.

The following error occurred converting from sym to double:

Unable to convert expression containing remaining symbolic

function calls into double array. Argument must be

expression that evaluates to number.

Error in DiffEq_alt (line 13)

out(1) = f(ti);

Ultimately, I need to be able to be able to declare y explicitly, but also treat it implicitly for when I differentiate the function with respect to t.

Answer 1

[Nipun]

Hi David,

I understand that you are trying to solve an ordinary differential equation (ODE) using symbolic mathematics in MATLAB, and you encounter an issue when attempting to evaluate a symbolic expression at specific numerical values for t and y(t). You want to keep y as a function of t for differentiation purposes but also need to substitute specific values for t and y(t).

To achieve this, you can use subs to substitute specific values into your symbolic expression before converting it to a numerical value. Here's how you can adjust your code to avoid the error:

To substitute a specific value for t and y(t), use the subs function. Let us say you want to evaluate f at t = ti and y(t) = wi. You can do this as follows:

ti = 1; % Example value for t
wi = 0.5; % Example value for y(t)

% Substitute the specific values into f
f_sub = subs(f, [t, y(t)], [ti, wi]);

After substituting the specific values, you can convert the result to a numerical value using double:

out(1) = double(f_sub);

This approach allows you to keep y as a function of t for differentiation and other symbolic operations, while also being able to evaluate f at specific numerical values for t and y(t).

Here is the combined snippet:

syms t y(t)
f = t^(-2) * (sin(2*t) - 2*t*y);

ti = 1; % Specific value for t
wi = 0.5; % Specific value for y(t)

% Substitute specific values into f and convert to numerical value
f_sub = subs(f, [t, y(t)], [ti, wi]);
out(1) = double(f_sub);

This should resolve the error and allow you to evaluate your symbolic expression at specific numerical values.

Hope this helps.

Regards,

Nipun