Penggunaan Edukasi Deret untuk Menyelesaikan Persamaan Diferensial Linear Orde Dua

Abstract

Differential equations are one of the compulsory subjects at state universities, especially in the mathematics education department. It is hoped that students can hone their skills to analyze, model, solve, and apply the theory they have learned to advanced theory. One of the second-order Linear Differential Equations challenging to solve is the second-order Linear Differential Equations with indeterminate coefficients. This equation is necessary to study because it has many applications in mathematics. This study examines the use of series education to solve second-order Linear Differential Equations, especially with indeterminate coefficients. The data were from calculus manuals and mathematicians in calculus. The research applied design research with the product of steps to solve the use of series reduction to solve second-order linear differential equations. The data were obtained through books, journals, and direct conversations with mathematicians in calculus and analyzed using the Milles and Huberman models and theoretical triangulation for the validity of the data. The achievement of this research is a second-order linear differential equation with an indeterminate coefficient that can be solved with a series, namely the Airy, Hermite, Chebyshev, Legendre, Bessel, Leguerre, and Gauss hypergeometric equations. These research findings can be used as input for mathematics teachers or students as an alternative work.