Order of a differential equation: why is it 2 in y′′ − 3y′ + 2y = 0?

[Dr Game]

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

$$y^(double prime)-3y^(prime)+2y = 0$$ 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]

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

$$y^(double prime)-3y^(prime)+2y = 0$$

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

Now, since the highest derivative in this equation is $$\frac{d^2y}{dx^2}$$ 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!

 

[Dr Game]

the following is an attachment of my notes:

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

 

[cristo]

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 $$\frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=0$$

Now, since the highest derivative in this equation is $$\frac{d^2y}{dx^2}$$ 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!

 

[Dr Game]

because I don't understand

 

[CPL.Luke]

think about it like the degree of a polynomial.

 

[Dr Game]

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