Question

Is this differential equation homogeneuos?
F(x,y,y',y'')=0
And how would look like nonhomogeneuos DE in this form?

Answer 1

Yes, a homogenous equation is equal to 0

Answer 2

and how would look like nonhomogeneuos?

Answer 3

a non-homogenous equation would equal some function of x or a constant

Answer 4

Ehhhh I'd be careful with this... F(x,y,y',y'') = y'' + y' + y + sin(x) = 0 is not homogeneous...

Answer 5

i know, but im interesting in this form....F(x,y',y'',..)=0....you have x here,maybe this is a constant?

Answer 6

ahh good point Jemurray3 i missed the x in there.

Answer 7

http://www.dummies.com/how-to/content/defining-homogeneous-and-nonhomogeneous-differenti.html

Answer 8

so, from this for you can only see its second order?

Answer 9

The definition for a homogeneous second order differential that I always would fall back on is something of the form
\[ a(x) y''(x) + b(x) y'(x) + c(x) y(x) = 0\]

Answer 10

differential equation*

Answer 11

Just so long as every term involves y or one of its derivatives, really.

Answer 12

but from this form you cant conclude if its homogeneuos or not?

Answer 13

F(x,y,y',y'') = 0 defines a second order, ordinary differential equation. That is all the information you can get from that.

Answer 14

ok, thanks