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

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,608

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: 20,349

Re: Homogeneous Differential Equations

Hi MathsIsFun,

The page on Homogeneous Differential Equations is well made.

Thanks, MathsIsFun!


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 102,844

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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,608

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: 102,844

Re: Homogeneous Differential Equations

Hi;

Nice page!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

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