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#1 2014-07-04 11:38:53

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Homogeneous Differential Equations

And another in the Diff Eq series: Homogeneous Differential Equations

The main weakness in this page is no explanation of why they are "Homogeneous". I played with linking f(zx,zy) = z^n f(x,y) to dy/dx=F(x/y) form but failed. If anyone knows a user-friendly way of explaining why "Homogeneous" that would be nice.

Comments, suggestions and error checking welcome.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2014-07-04 12:02:48

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,851

Re: Homogeneous Differential Equations

Hi MathsIsFun,

The page on Homogeneous Differential Equations is well made.

Thanks, MathsIsFun!


Character is who you are when no one is looking.

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#3 2014-07-04 21:36:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,002

Re: Homogeneous Differential Equations

Hi;

First example can have a negative solution also. Second example is correct. You can solve for y in the third example.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#4 2014-07-04 23:09:31

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: Homogeneous Differential Equations

Thanks bobby ... yes and yes: ±√(2x^2+c) − x is what I get now.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2014-07-05 01:19:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,002

Re: Homogeneous Differential Equations

Hi;

Nice page!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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