Question

Need help finding order and degree for the question below:

Answer 1

\[\LARGE [\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}]^{3/2}=y\]

My doubt is why squaring does not give me the required answer?

Answer 2

well, if you square does it rid you of the exponent on your differentials?

Answer 3

(3/2)*2=1 so yeah?

Answer 4

check your math real quick

Answer 5

lol did I make a silly mistake? :O

Answer 6

yea, (3/2)*2=3

Answer 7

but def have the right idea

Answer 8

So then I get order 2 and degree 3?

Answer 9

that's what I'm getting

Answer 10

But the solution given is raising power to 2/3 and hence order 2 and degree 1.

Answer 11

well, you could do that too. Which is simpler

Answer 12

usually you want the simplest form for the canonical

Answer 13

But I need a real reason to justify the actual answer.

Answer 14

Oh, well you want to reduce it as much as possible to make it easiest to solve. Eradicating the degree, makes the problem easier

Answer 15

technically both could be correct, but the simplest form is degree 1 and order 2

Answer 16

hmm..I am still not satisfied :| maybe I should add simplest form to the definition of degree in my notes.

Answer 17

let me see if I can dig up a good reason

Answer 18

Thanks :)

Answer 19

So side note: This is really awesome quick reference I found http://www.sosmath.com/tables/diffeq/diffeq.html Also check out how to solve ODEs using complex variables, it's pretty sick method.

Answer 20

That doesn't explain finding order. It is about solving differential equations.

Answer 21

I know, but I just liked it for future reference. Here is a new book you could take a look at, but unfortuanately, I am unable to find any similar examples that make it easier other than adjusting the prompt to determine the simplest order and degree of the following dif eq. http://www.textbooksonline.tn.nic.in/books/12/std12-bm-em-2.pdf

Answer 22

Okay thanks for trying

Answer 23

np, but I would just say do reduce the polynomial as much as possible since you are unable to have mixed derivatives and be able to solve

Answer 24

ie Y''Y' is not ok, which if you have any sort of power on that particular problem, would exist

Answer 25

Maybe that would be an adequate reason to get rid of the exponent completely

Answer 26

Have you tried using Conflict Resolution skills on your equation?

Answer 27

The order is the highest derivative, here it's 2.
The degree is the power on the highest derivative. Since it's not in that form, you have to arrange it to algebraically show that. \[(y''+y')^{3/2}=y\] \[y''+y'=y^{2/3}\]This is the form you need. If you only square root both sides and then make it look like this by multiplying out the cube, it's wrong because your second derivative isn't isolated. \[(y'')^3+3(y'')^2y'+3y''(y')^2+(y')^3=y^2\] There's no power on "the" highest derivative since it's spread out among 3 terms.

So the degree is 1 here.

Answer 28

Oh now that makes sense. Thanks a lot @Kainui and @FibonacciChick666

Answer 29

Can I get a "thank you."