A general solution contains any constant, and a special solution refers to a specific constant. For example, y = 4x 2 is a special solution of xy' = 8x 2, but y = 4x 2+c is a general solution of xy' = 8x 2, where c is an arbitrary constant.

There are many methods to find the general solution of differential equation, such as characteristic line method, separation of variables method, special function method and so on. For non-homogeneous equations, the special solution of any non-homogeneous equation can be added to the general solution of a homogeneous equation to get the general solution of the non-homogeneous equation.

Differential equation function

1. Differential equation is the most important branch of higher mathematics. As long as the equation contains the relationship between the derivative of unknown quantity and variables, it can be called differential equation.

2. We can divide a complex individual into infinite tiny parts by differential equation, then solve the boundary conditions of each tiny part by differential equation, and finally get the solution of the whole part.

3. Differential equations are now widely used in computer simulation, electronic circuit calculation, aerospace and other fields.