anonymous
  • anonymous
Is this differential equation homogeneuos? F(x,y,y',y'')=0 And how would look like nonhomogeneuos DE in this form?
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Yes, a homogenous equation is equal to 0
anonymous
  • anonymous
and how would look like nonhomogeneuos?
anonymous
  • anonymous
a non-homogenous equation would equal some function of x or a constant

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anonymous
  • anonymous
Ehhhh I'd be careful with this... F(x,y,y',y'') = y'' + y' + y + sin(x) = 0 is not homogeneous...
anonymous
  • anonymous
i know, but im interesting in this form....F(x,y',y'',..)=0....you have x here,maybe this is a constant?
anonymous
  • anonymous
ahh good point Jemurray3 i missed the x in there.
anonymous
  • anonymous
http://www.dummies.com/how-to/content/defining-homogeneous-and-nonhomogeneous-differenti.html
anonymous
  • anonymous
so, from this for you can only see its second order?
anonymous
  • anonymous
The definition for a homogeneous second order differential that I always would fall back on is something of the form \[ a(x) y''(x) + b(x) y'(x) + c(x) y(x) = 0\]
anonymous
  • anonymous
differential equation*
anonymous
  • anonymous
Just so long as every term involves y or one of its derivatives, really.
anonymous
  • anonymous
but from this form you cant conclude if its homogeneuos or not?
anonymous
  • anonymous
F(x,y,y',y'') = 0 defines a second order, ordinary differential equation. That is all the information you can get from that.
anonymous
  • anonymous
ok, thanks

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