Mathematical physical equations refer to some partial differential equations (sometimes including integral equations and some ordinary differential equations) which are obtained after some simplification in physics, mechanics, engineering technology and other problems and reflect the relationship between physical quantities in the objective world.

It should be pointed out that these equations describing universal laws (also known as universal equations) can only be solved by adding certain initial conditions and boundary conditions. The universal definite equation and the definite solution conditions constitute the definite solution problem.

For convenience, this paper takes wave equation as an example to discuss several common solutions of mathematical equation.

These solutions include traveling wave method, variable separation method and integral transformation method.

The main solutions include:

1. Traveling wave method

2. Separation of variables method

3. Integral transformation method

4. Green's function method

5. Variational method.