Analytical solutions, also called closed-form solutions, are mathematical solutions in the form of math expressions. If you are developing algorithms or modeling engineering systems, analytical solutions often offer important advantages:

- Transparency: Because analytical solutions are presented as math expressions, they offer a clear view into how variables and interactions between variables affect the result.
- Efficiency: Algorithms and models expressed with analytical solutions are often more efficient than equivalent numeric implementations. For example, to compute the solution of an ordinary differential equation for different values of its parametric inputs, it is often faster, more accurate, and more convenient to evaluate an analytical solution than to perform numerical integration.

Learn more about calculating analytical solutions with MATLAB and Symbolic Math Toolbox.

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*See also*: *MuPAD*, *mathematical modeling*, *analytical solution videos*