If you missed the previous article in the series you can find it here: Differential Equations 31: The Wronskian Method If you missed the previous article in the series you can find it here:medium.com The Frobenius Method There are second-order linear ODE’s that appear in physical applications which do not have two linearly independent analytic solutions about t=0. The Bessel equation is perhaps the most thoroughly studied example; it is surely the most…

If you missed the previous article in the series you can find it here: Differential Equations 30: Bessel’s Equation If you missed the previous article in the series you can find it here:medium.com The Wronskian Method All of the ODE’s we have studied, and a great many more that have singular points at t=0, have the form

If you missed the previous article in the series you can find it here: Differential Equations 29: Three Important Application Examples If you missed the previous article in the series you can find it here:medium.com Bessel’s Equation The Bessel ODE

If you missed the previous article in the series you can find it here: Differential Equations 28: Legendre’s Equation If you missed the previous article in the series you can find it here:medium.com Three Important Examples In this article, we will present three examples that find application in several areas of applied physics. First, we find polynomial solutions for the Hermite equation

If you missed the previous article in the series you can find it here: Differential Equations 27: Power Series Solutions of Linear Differential Equations Pt. 2 If you missed the previous article in the series you can find it here:medium.com Legendre’s Equation An ODE is often encountered when modelling physical phenomena in spherical coordinates is the Legendre equation,

If you missed the previous article in the series you can find it here: Differential Equations 26: Power Series Solutions of Linear Differential Equations If you missed the previous article in the series you can find it here:medium.com Power Series Solutions Consider this linear equation with variable coefficients:

If you missed the previous article in the series you can find it here: Differential Equations 25: Taylor Series of Analytic Functions If you missed the previous article in the series you can find it here:medium.com Power Series Solutions of Linear Differential Equations In this article, we show how to use the theory of the Taylor series to find solutions of linear homogeneous ODE’s where the coefficients are functions of t. Consider the linear ODE

If you missed the previous article in the series you can find it here: Differential Equations 24: Series Methods & Analytic Functions If you missed the previous article in the series you can find it here:medium.com Taylor Series of Analytic Functions Suppose that f(t) is analytic at t=0. The sums

If you missed the previous article in the series you can find it here: Differential Equations 23: The Solution of Initial-Value Problems & The Laplace Transform of… If you missed the previous article in the series you can find it here:medium.com Series Methods The solutions of constant-coefficient homogeneous ODE’s are combinations of polynomials and exponential functions. By contrast, the Cauchy-Euler equation, a linear ODE with variable coefficients, has solutions that may involve ln(t) as well as sums of various…