Orders and Degrees

  • Thread starter Dr Game
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26
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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?
 

cristo

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

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!
 
26
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the following is an attachment of my notes:

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

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cristo

Staff Emeritus
Science Advisor
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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!


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!
 
26
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because I don't understand
 
441
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think about it like the degree of a polynomial.
 
26
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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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