11. Cauchy–Euler Equation

This chapter delves into the Cauchy–Euler equation, a type of differential equation characterized by the power of the independent variable matching the order of the derivative. The chapter begins by introducing the general form of the equation and demonstrating how to convert it into a linear differential equation with constant coefficients. It then explores various examples, ranging from second-order to higher-order equations, providing both analytical solutions and MATLAB implementations for validation. The chapter also covers non-homogeneous equations and demonstrates how to find particular solutions. Additionally, it addresses boundary value problems and provides exercises for further practice. The use of MATLAB throughout the chapter not only validates the solutions but also offers a practical approach to solving these equations, making it a valuable resource for professionals who need to apply these concepts in their work.