ABSTRACT
In this chapter, we present analytical and numerical methods for solving linear ODEs by hand and using Python. We examine both first order and second order ODEs, focusing on physically motivated applications such as the simple plane pendulum, RLC circuits, and the driven damped harmonic oscillator. We conclude the chapter with series solutions methods to solve the Legendre Equation, Associated Legendre Equation, and Bessel's equation. We show how to use Python to evaluate Legendre polynomials, associated Legendre functions, and Bessel functions.
