Higher order differential equations : Euler cauchy equation

Euler–Cauchy Differential Equation is one of the most important topics in Differential Equations for GATE, ESE, and university exams. In this video, I explain how to identify, convert, and solve Euler–Cauchy ODEs using a simple step-by-step approach with solved examples. What you will learn in this video: ✔ What is Euler–Cauchy Differential Equation ✔ Why it is also called Equidimensional Equation ✔ How to convert it into a constant-coefficient differential equation ✔ Substitution method: Who should watch this video? – GATE 2026 Aspirants – ESE/IES students – B.Tech / Engineering Mathematics learners – Anyone practicing ODEs for competitive exams✔ How to solve the characteristic equation ✔ Special cases where repeated roots occur ✔ Complete solution with examples for GATE-level problems