Cauchy-Euler Equation General Form
The differential equation,
[Tex]\bold{a_nx^ny^{(n)}+a_{n-1}x^{n-1}y^{n-1}+…+a_0y}[/Tex]
is called the Cauchy Euler differential equation of order n.
Where yn represents the nth derivative of y with respect to x, ai, i = 0, . . . , n are constants and an ≠ 0.
Cauchy-Euler Equation Examples
Here are some examples of Cauchy-Euler equations:
- x2y” +y=0
- x2y” + 4y=0
- x2y” -3xy’ – 7y =0
- x3y” – 2x2y’ + xy =0
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
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