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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

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.

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,410

Re: Homogeneous Differential Equations

Hi MathsIsFun,

The page on Homogeneous Differential Equations is well made.

Thanks, MathsIsFun!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Homogeneous Differential Equations

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

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Homogeneous Differential Equations

Hi;

Nice page!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.