Characteristic equation (calculus)

In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree ${\displaystyle n}$ upon which depends the solution of a given ${\displaystyle n\,}$th-order differential equation or difference equation. The characteristic equation can only be formed when the differential or difference equation is linear and homogeneous, and has constant coefficients. Such a differential equation, with ${\displaystyle y\,}$ as the dependent variable and ${\displaystyle a_{n},a_{n-1},\ldots ,a_{1},a_{0}}$ as constants,

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