Identifying the Degree of a Differential Equation

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Discussion Overview

The discussion centers on defining the degree of a differential equation, specifically examining the degree of a given ordinary differential equation (ODE) expressed in terms of its derivatives. The scope includes theoretical understanding and clarification of concepts related to differential equations.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions how to define the degree of a differential equation and presents a specific ODE for analysis.
  • Another participant asserts that the degree is the power of the highest order derivative in the equation and asks for clarification on the degree of the provided ODE.
  • A third participant reiterates the definition of degree as the power of the highest order derivative but introduces a conflicting viewpoint based on their math teacher's explanation, suggesting that the degree should be the sum of the exponents of its variables, leading to a total of five.
  • A later reply focuses on the highest order derivative in the equation, stating that it has a degree of two, thus concluding that the degree of the ODE is two.

Areas of Agreement / Disagreement

Participants express differing views on the definition of the degree of a differential equation, with some supporting the idea that it is based solely on the highest order derivative, while others argue for a definition that includes the sum of exponents from all terms. The discussion remains unresolved regarding which definition is correct.

Contextual Notes

There is ambiguity regarding the definitions of degree in the context of differential equations, as well as the application of these definitions to the specific ODE presented. The discussion highlights differing interpretations that depend on the definitions used.

KD1729
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How Can we define the degree of differential equation ?
What is the degree of $$\left(\frac{{d}^{2}y}{d{x}^{2}}\right)^{\!{2}}\left(\frac{dy}{dx}\right)^{\!{3}} +\left(\frac{dy}{dx}\right)^{\!{1}} =0$$ ??(Wondering)
 
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The degree of a differential equation is the power of the highest order derivative in the equation. Based on this what would you say the degree of the given ODE is?
 
MarkFL said:
The degree of a differential equation is the power of the highest order derivative in the equation. Based on this what would you say the degree of the given ODE is?

Then it Should be one.

But, My maths Teacher said it is equal to the 2+3=5.
He said that for any term degree is the sum of exponents of its variables & degree of a equation is the highest degree term. Which is right ?(Sadface)
 
I would look at the derivative in red:

$${\color{red}\left(\frac{{d}^{2}y}{d{x}^{2}}\right)^{\!{2}}}\left(\frac{dy}{dx}\right)^{\!{3}} +\left(\frac{dy}{dx}\right)^{\!{1}} =0$$

This is the highest order derivative present in the equation and the degree of this derivative is two, thus I would say the degree of the ODE is two.
 

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