matlab unable to solve symbolically. returning a numeric solution using vpasolve.

In MATLAB, if the symbolic solver is unable to find a closed-form solution for an equation, you can use the `vpasolve` function to obtain a numerical solution instead. `vpasolve` stands for "Variable Precision Arithmetic Solve" and it can handle equations involving both symbolic and numeric variables.

To use `vpasolve`, you need to define your equation as a symbolic expression using the `syms` function, specify the variables you want to solve for, and then call `vpasolve` with the equation and initial guesses for the variables. Here's an example:

syms x y
eqn = x^2 + y^2 == 1;
sol = vpasolve(eqn, [x, y], [0.5, 0.5]);

In this example, `eqn` represents the equation x^2 + y^2 = 1. The `vpasolve` function is called with the equation, the variables to solve for (x and y), and initial guesses for the variables ([0.5, 0.5]). The `sol` variable will store the numerical solutions.

Keep in mind that `vpasolve` can be slower than the symbolic solver, especially for complex equations or large systems of equations. It is also worth noting that the numerical solutions obtained using `vpasolve` might have limited precision compared to exact symbolic solutions.