y(0)=A y'(0)=B (2)

This is the initial value problem of second-order linear ordinary differential equations with constant coefficients.

Firstly, the special solution of the nonhomogeneous equation (1) is obtained: y * (x); When finding the general solution of the homogeneous equation (1): ay''+by'+cy = 0 (3), there are two undetermined coefficients in the general solution, which are determined by the initial condition (2). Finally, the general solution y(X) of (1) is obtained:

The special solution of y(x)=( 1)+the general solution of (3).