37 results about "Characteristic equation" patented technology

In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given nth-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 y as the dependent variable, superscript (n) denoting nᵗʰ-derivative, and aₙ, aₙ ₋ ₁, ..., a₁, a₀ as constants, aₙy⁽ⁿ⁾+aₙ₋₁y⁽ⁿ⁻¹⁾+⋯+a₁yʼ+a₀y=0, will have a characteristic equation of the form aₙrⁿ+aₙ₋₁rⁿ⁻¹+⋯+a₁r+a₀=0 whose solutions r₁, r₂, ..., rₙ are the roots from which the general solution can be formed.