Lesson Plan: Cauchy–Euler Differential Equation
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to solve Cauchy–Euler differential equations of the general form 𝑎_𝑛 𝑥^𝑛 𝑦^(𝑛) + 𝑎_𝑛−1 𝑥^𝑛−1 𝑦^(𝑛−1) + ⋯ + 𝑎₀ 𝑦 = 𝑓(𝑥).
Objectives
Students will be able to
- recognize Cauchy–Euler differential equations,
- solve Cauchy–Euler differential equations using substitution,
- solve Cauchy–Euler differential equations using an ansatz/trial solution,
- solve initial-value problems involving Cauchy–Euler differential equations.
Prerequisites
Students should already be familiar with
- differentiation,
- integration,
- homogeneous linear ODEs with constant coefficients.
Exclusions
Students will not cover
- other types of differential equations.