METHOD OF UNDETERMINED COEFFICIENTS IN SOLVING THIRD-ORDER LINEAR DIFFERENTIAL EQUATIONS: A COMPREHENSIVE ANALYSIS - Aprecio, Noel Victor; Roy Jr., Federico (Journal of Engineering & Technological Advances, 2024)
Higher-order linear differential equations have great significance theoretically and practically. This paper solves a third-order linear differential equation with constant coefficients by method of undetermined coefficients. Its strengths and limitations were analysed. Analysis suggests that the method of undetermined coefficients requires that the inhomogeneous term be algebraic, exponential, or sinusoidal functions only. Additionally, if the inhomogeneous term is a solution of the differential equation itself, may yield a linear combination of . In such case, the prediction for will be modified by multiplying the variable however many times necessary.