what is a symbolic variable, and how is it used? in matlab

In MATLAB, a symbolic variable is a variable that can hold a symbolic expression or a mathematical formula, unlike a numeric variable that can hold only one numeric value at a time.

To create a symbolic variable in MATLAB, you need to use the sym function as shown below:

main.m
syms x y        % declares x and y as symbolic variables
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Once you have declared a symbolic variable, you can use it to manipulate algebraic expressions symbolically. For example, you can perform algebraic operations using the symbolic variables, as shown below:

main.m
syms x y
a = x^2 + 2*x*y + y^2     % expression with symbolic variables
b = expand(a)             % expands expression
c = simplify(a)           % simplifies expression
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In the above example, we have created two symbolic variables, x and y, and used them to define an algebraic expression a. We have then used the expand function to expand the expression and the simplify function to simplify it.

The symbolic variables are often used in MATLAB for symbolic computations, such as solving equations with symbolic variables or computing derivatives and integrals.

main.m
syms x
f = x^2 + 3*x + 2      % function with symbolic variable
dfdx = diff(f, x)      % first derivative of function
int_f = int(f,x)       % integral of the function
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