Author(s)

Ling Hao

Corresponding Author

Ling Hao

ABSTRACT

First-order linear differential equations are an important class of ordinary differential equations. They are the simplest differential equations with general solutions, generally can be expressed as dy/dx=p(x)y+q(x). The complex geometry method is used to study the properties of the singularity of the first-order linear differential equation on the complex plane, prove that the singularity can only be on the x-axis, and calculate the eigenvalues of the singularity. At the same time, we proved that under sufficiently general conditions, the eigenvalues of the singularities are equal to the residues of p(x). At this time, the eigenvalues of all the singularities of the equation satisfy the same overall properties as the residues of p(x).

KEYWORDS

Ordinary differential equations, singular point multiplicity, complex geometry method