The second-order linear differential equation with constant coefficients is a differential equation in the form of y''+py'+qy=f(x), where p and q are real constants. When the free term f(x) is a continuous function defined on the interval I, that is, y''+py'+qy=0, it is called a second-order homogeneous linear differential equation with constant coefficients.

Standard format y "+py'+QY = 0.

Characteristic equation R 2+PR+Q = 0.

Introduction.

The definition of differential in mathematics: from the function B=f(A), two groups of numbers A and B are obtained. In A, when dx approaches itself, the limit of the function at dx is called the differential of the function at dx, and the central idea of the differential is infinite division. Differential is the linear main part of function change. One of the basic concepts of calculus.

Usually, the increment Δ x of the independent variable X is called the differential of the independent variable, which is denoted as dx, that is, dx = Δ x. Then the differential of the function y = f(x) can be written as dy = f'(x)dx. The quotient of the differential of the dependent variable and the differential of the independent variable of a function is equal to the derivative of the function. Therefore, the derivative is also called WeChat business.