Characteristic equation (calculus)
In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree ![n \,](/Images/godic/202412/22/a957404c96e59f1746f97ab668c8e1f83913.png")
on which depends the solutions of a given -order differential equation. The characteristic equation can only be formed when the differential equation is linear, homogeneous, and has constant coefficients. Such a differential equation, with ![y \,](/Images/godic/202412/22/ec9ff0a12771e750c2685d3b89a37c793913.png")
as the dependent variable and ![a_{n}, a_{n-1}, \ldots , a_{1}, a_{0}](/Images/godic/202412/22/3092da3821b6a4b898ef962aef17dce43913.png")
as constants,