Second Order Cauchy-Euler Equation
The most common Cauchy–Euler equation is the second-order equation, appearing in a number of physics and engineering applications, such as when solving Laplace’s equation in polar coordinates. It is given by the equation:
[Tex]\bold{a_2x^{2}{\frac {d^{2}y}{dx^{2}}}+a_1x{\frac {dy}{dx}}+a_0y=0}[/Tex]
Cauchy Euler Equation
Cauchy-Euler equation, also known as the Euler-Cauchy equation, is a type of linear differential equation with variable coefficients. It has the general form [Tex] x^n y^{(n)} + a_{n-1} x^{n-1} y^{(n-1)} + \cdots + a_1 x y’ + a_0 y = 0[/Tex]. It’s named after two famous mathematicians, Cauchy and Euler. This equation is special because it helps us understand how things change over time or space. It’s like a key that unlocks the secrets of many natural processes, like how objects move or how electricity flows.
In this article, we’ll break down what the Cauchy-Euler equation is all about, how to solve it, and where we can see it in action in the real world.
Table of Content
- What is Cauchy-Euler equation?
- Cauchy-Euler Equation Examples
- How to Solve the Cauchy-Euler Differential Equation?
- Cauchy-Euler Equation Solved Problems
- Cauchy Euler FAQs