Variation of Parameter Method for Solving Homogeneous Second Order Linear Ordinary Differential Equations

Daniel Arficho

doi:10.4172/2168-9679.1000258

Abstract

In this manuscript, we introduce variation of parameter method for solving homogeneous linear second order ordinary differential equations with constant coefficients. Moreover, we derive general solution method to solve homogeneous linear second order ordinary differential equations with constant coefficients.

Highlights

A differential equation is an equation that relates an unknown function and one or more of its derivatives of with respect to one or more independent variables [1]
We introduce variation of parameter method to find general solution of homogeneous second order linear ordinary differential equation with constant coefficients
If we replace a scalar m by a function u(x) and assume that y = exp ∫u(x)dx is solution of homogeneous second order linear ordinary differential equation with constant coefficients, y = exp ∫u(x)dx is variation of parameter method for solving second order linear ordinary differential equation with constant coefficients, where u(x) is a function of x to be determined

Summary

Introduction

A differential equation is an equation that relates an unknown function and one or more of its derivatives of with respect to one or more independent variables [1]. Most authors of differential books used this technique to derive solution method for solving second order linear ordinary differential equation with constant coefficients. We apply Moivre’s theorem to find general solution of ay(2)+by(1)+cy=0 when b2-4ac

Motivation Research Questions

Results and Discussion

Conclusion