Understanding Orders & Degrees in an Equation

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Discussion Overview

The discussion revolves around understanding the concept of order in differential equations, specifically in the context of the equation y'' - 3y' + 2y = 0. Participants explore definitions, interpretations, and potential misunderstandings regarding the order and its relation to derivatives.

Discussion Character

  • Conceptual clarification, Debate/contested, Technical explanation

Main Points Raised

  • Some participants assert that the order of a differential equation is defined as the highest derivative present in the equation, which in this case is the second derivative, making it a second order differential equation.
  • One participant questions the definition by suggesting that the order could be interpreted differently, specifically mentioning a possible confusion with coefficients and the number of derivatives taken.
  • Another participant expresses uncertainty about the order being 2 and not -3, indicating a potential misunderstanding of the concept.
  • A later reply suggests thinking about the order in relation to the degree of a polynomial, implying a connection between the two concepts.
  • One participant reflects on their initial misunderstanding, indicating they thought the order was related to the result of derivatives rather than the count of how many times to derive.

Areas of Agreement / Disagreement

There is no clear consensus on the interpretation of the order of the differential equation, with some participants affirming the standard definition while others express confusion or alternative views.

Contextual Notes

Some participants appear to conflate the concepts of order and the coefficients of derivatives, leading to misunderstandings about the definition of order in differential equations.

Dr Game
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I was taking notes in class and the prof said that in the equation

[tex]y^(double prime)-3y^(prime)+2y = 0[/tex] that 2 was the order.. is that due to the following?

the first y = 0 when you take the derivative twice
the second y = 0 when you derive it once
and the first one = 2 when you derive it once

Just a question.. shouldn't I derive the first one 3 time, and the second one 2 times, because you derive 2y once?
 
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The order of a differential equation is defined as the highest derivative that the equation contains.

Dr Game said:
I was taking notes in class and the prof said that in the equation

[tex]y^(double prime)-3y^(prime)+2y = 0[/tex]
Let's rewrite this as [tex]\frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=0[/tex]

Now, since the highest derivative in this equation is [tex]\frac{d^2y}{dx^2}[/tex] the equation is a second order differential equation.

the first y = 0 when you take the derivative twice
the second y = 0 when you derive it once
and the first one = 2 when you derive it once

Just a question.. shouldn't I derive the first one 3 time, and the second one 2 times, because you derive 2y once?

I'm not really sure what you're doing here!
 
the following is an attachment of my notes:

I don't get why the order is 2 and not -3
 

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Dr Game said:
the following is an attachment of my notes:

I don't get why the order is 2 and not -3

Well, read my above post!


cristo said:
The order of a differential equation is defined as the highest derivative that the equation contains.


Let's rewrite this as [tex]\frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=0[/tex]

Now, since the highest derivative in this equation is [tex]\frac{d^2y}{dx^2}[/tex] the equation is a second order differential equation.

Why do you think that the order is -3? The only way I can see you getting this is by looking at the coefficient in front of the y' term, and I'm not sure why you're doing that!
 
because I don't understand
 
think about it like the degree of a polynomial.
 
you know what... I thought it was the number that comes out after you derive it a few times.. not how many times you derive it

i get it now, thanks
 

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