The general solution is y = e [-∫ p (x) dx] {∫ q (x) e [∫ p (x) dx] dx+c},

The method adopted is to solve the homogeneous equation first, and then solve the non-homogeneous equation by parameter variational method;

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Differential equations developed by calculus. Newton and Leibniz, the founders of calculus, both dealt with problems related to differential equations in their works. 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.

The research on differential equations in the field of mathematics focuses on several different aspects, but most of them are related to the solutions of differential equations. Only a few simple differential equations can be solved analytically. However, even if the analytical solution is not found, some properties of the solution can still be confirmed. When the analytical solution cannot be obtained, the numerical solution can be found by means of numerical analysis and computer. ? Dynamic system theory emphasizes the quantitative analysis of differential equation system, and many numerical methods can calculate the numerical solution of differential equation with certain accuracy.