On the differential equation $y" - (b'(x)/2b(x))y' + \lambda b(x)y = 0$

TL;DR

This paper discusses solving a specific second order linear differential equation using the Hamilton-Jacobi method, highlighting the existence of equations solvable via characteristic equations.

Contribution

It presents a Hamilton-Jacobi approach for solving a class of second order linear differential equations, linking solutions to characteristic equations.

Findings

Hamilton-Jacobi method effectively solves the differential equation.

Existence of equations solvable through characteristic equations.

Method provides a new perspective on solving certain second order ODEs.

Abstract

The Hamilton-Jacobi method which can be used for solving this equation has been presented. The solution of the equation suggests that there exist some second order linear ordinary differential equations whose resolution can be done by means of characteristic equation.