Question

How to identify Cauchy-Euler equation?

a) By looking for a linear combination of terms
b) By checking for constant coefficients
c) By observing exponential functions
d) By examining trigonometric functions

Answer 1

The Cauchy-Euler equation is a second-order linear homogeneous differential equation with variable coefficients. It can be identified by observing the exponents on the terms in the equation. Correct option is c)

Step-by-step explanation:

The Cauchy-Euler equation is a second-order linear homogeneous differential equation with variable coefficients. It can be identified by observing the exponents on the terms in the equation.

A Cauchy-Euler equation can be written in the form:

ax^2y'' + bxy' + cy = 0

where a, b, and c are constants and y is a function of x.

By examining the exponents on the terms, you can determine if it is a Cauchy-Euler equation. The exponents on the terms should satisfy the following condition:

m(m-1)a + mb + c = 0