Second order linear homogeneous equations with constant coefficients

Abstract

Differential equations are a great way for readers to understand the relationship between mathematics and the physical sciences or engineering. Before engineers or students can focus on the applications of differential equations or study them, it is necessary to learn the different methods of solving differential equations. The main goal of this research is to find the specific equation for a second-order homogeneous linear differential equation with constant coefficients and to obtain the general solution of the given differential equation by finding the roots of the specific equation. To conduct this research, the library method was used, which utilized various books and reliable sources. As a result, a comprehensive study was conducted for the specific equation (second-order homogeneous linear differential equation with constant coefficients). In this study, different situations for the general solution of (second-order homogeneous linear differential equations with constant coefficients) have been investigated. For example, if the specific equation of a second-order homogeneous linear differential equation with constant coefficients has two different roots, has two equal roots, or has mixed roots.