Understanding Orders & Degrees in an Equation

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In summary, the conversation discusses the concept of order in differential equations. The equation given is a second order differential equation because the highest derivative is y'' and the order is defined as the highest derivative in the equation. The confusion arises when trying to find the order by looking at the coefficients, but the order is based on the highest derivative in the equation.
  • #1
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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  • #2
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!
 
  • #3
the following is an attachment of my notes:

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

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  • #4
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!
 
  • #5
because I don't understand
 
  • #6
think about it like the degree of a polynomial.
 
  • #7
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
 

1. What is the difference between orders and degrees in an equation?

The order of an equation refers to the highest exponent or power of the independent variable. For example, in the equation y = 2x^3 + 5x^2 + 8, the order is 3. The degree, on the other hand, refers to the sum of all the exponents in the equation. In this case, the degree is 5 (3+2).

2. How do you determine the order of an equation?

To determine the order of an equation, you need to look at the highest exponent of the independent variable. For example, in the equation y = 2x^3 + 5x^2 + 8, the order is 3 because x is raised to the power of 3, which is the highest exponent.

3. What is the significance of orders and degrees in an equation?

The orders and degrees of an equation are important because they give us information about the behavior and complexity of the equation. Higher orders and degrees indicate that the equation is more complex and may have multiple solutions, while lower orders and degrees indicate a simpler equation with fewer solutions.

4. Can an equation have different orders and degrees?

Yes, an equation can have different orders and degrees. This can happen when there are multiple variables in the equation, and each variable has a different exponent. For example, the equation y = 2x^3 + 5x^2 + 8z^4 has an order of 3 for x and an order of 4 for z, with a total degree of 7 (3+4).

5. How do orders and degrees affect the graph of an equation?

The orders and degrees of an equation can affect the shape and behavior of its graph. Higher orders and degrees can result in more complex and curved graphs, while lower orders and degrees can result in simpler and straighter graphs. Additionally, the number of solutions of an equation can also be determined by its orders and degrees.

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