The expression of the first-order nonhomogeneous linear differential equation is y'+p (x) y = q (x); The expression of second-order non-homogeneous linear differential equation with constant coefficients is y''+py'+qy=f(x). The study of non-homogeneous linear differential equation is actually the study of its solution, and its general solution is composed of the general solution of its corresponding homogeneous equation plus a special solution.

Differential equations are widely used and can solve many problems related to derivatives. Many kinematics and dynamics problems involving variable forces in physics, such as falling bodies with air resistance as speed function, can be solved by differential equations. In addition, differential equations have applications in chemistry, engineering, economics and demography.

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.