Question

"The differential equation is not a polynomial equation in its derivatives and so its degree is not defined."

What does "polynomial equation in its derivatives" mean?

I don't understand, how do we decide when the degree of a differential equation is undefined.

Answer 1

a polynomial degree is defined by its highest exponent. The degree of a differential equation is not related to the degrees of its polynomial parts.

Answer 2

There are certain cases when the degree of a differential equation is undefined. How do I determine that in a differential equation the degree is undefined?

Answer 3

hmm, id have to google that one ... i do know that:

order is the higest derivative; and degree is the exponent of the highest order

[y^(4)]^2 + y1 = sin(x)

has order 4, and degree 2; but when is degree undefined? maybe when it is a variable?

Answer 4

http://books.google.com/books?id=SVp7QE8xHJwC&pg=SA23-PA8&lpg=SA23-PA8&dq=degree+undefined+differential+equation&source=bl&ots=Y4Q0CcQ6fn&sig=VNkijjdjVp3kGe0KaOY0qP2AJHk&hl=en&sa=X&ei=b3SoUpOVMcnckQf2sIGABg&ved=0CE4Q6AEwBQ#v=onepage&q=degree%20undefined%20differential%20equation&f=false

check out these solutions

Answer 5

yeah, it appears that if something other than a numerical exponent is playing with a derivative part; then the degree cannot be determined

Answer 6

@amistre64 I have figured out that the degree is undefined when either the exponent is a derivative or there is something like sin(dy/dx) given.

Just as

x^2 + 1 = 0 is a polynomial
but x^2 + sin(x) =0 is not

Answer 7

sounds reasonable to me :)