Aruwin
Aruwin
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11 Feb 2012

Homogeneous function

Function f (x, y) is a homogeneous expression if f (tx, ty) = (t^n) * f (x, y), for t (≠0). Prove that a homogeneous expression f (x, y) satisfies the following partial differential equation where p is a natural number .

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circularsquare

circularsquare

Branch Unspecified
11 Feb 2012
There is an alternative definition of homogeneous function of order n.
I.e f(x,y) = (x^n)u(y/x) where u is a function of y/x.

Example :- consider f(x,y) = x^2 + xy + y^2 you can write it as
(x^2) (1 + y/x + (y/x)^2 ).

Use this property to prove for case p = 1. Then use mathematical induction on p.

Proving it is beyond my ability as there are many calculations. 😀 . Keep trying.
Aruwin

Aruwin

Branch Unspecified
11 Feb 2012
circularsquare
There is an alternative definition of homogeneous function of order n.
I.e f(x,y) = (x^n)u(y/x) where u is a function of y/x.

Example :- consider f(x,y) = x^2 + xy + y^2 you can write it as
(x^2) (1 + y/x + (y/x)^2 ).

Use this property to prove for case p = 1. Then use mathematical induction on p.

Proving it is beyond my ability as there are many calculations. 😀 . Keep trying.
I hate doing proving problems but I am gonna try it anyway. Well, can you look at my other thread? I guess that's easier than this.
11 Feb 2012
By any chance is this a homework?
Aruwin

Aruwin

Branch Unspecified
11 Feb 2012
Praveen-Kumar
By any chance is this a homework?
Nope,not homework. I have never posted any homework on here. If it was homework, I would leave it blank and wait until the teacher discuss it in class.
11 Feb 2012
Okay... 😀
Aruwin

Aruwin

Branch Unspecified
11 Feb 2012
Praveen-Kumar
Okay... 😀
And as to why I always post questions on here is because people here explain better than the teachers at my university do.
12 Feb 2012
Aruwin
And as to why I always post questions on here is because people here explain better than the teachers at my university do.
Ah! That's nice... Sure, we would be able to help you out... 😀

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