I see where this is bit is from, so great!

For this part, what are tx and ty? It's just that the DE in question is using y's and x's.Quote:

It is homogeneous if we can observe the following:

AND .

Is t a dummy variable or something?

Printable View

- October 7th 2008, 02:06 PMShowcase_22
- October 7th 2008, 02:19 PMChris L T521
Sorta. The variable t is like a dummy variable, but its something that can help us show [analytically] if the functions M(x,y) and N(x,y) [from the DE] in question are homogeneous.

If we introduce this dummy variable t and show that if we have after manipulating we're almost done showing that its homogeneous. The last part is to show that we get after manipulating AND that the we have the same exponents. If the exponents are different, OR we can't show that or , then its not homogeneous.

Does this help?

--Chris - October 8th 2008, 12:42 AMShowcase_22
I think i'm understanding it, but there's just something else that's puzzling.

We have:

and we're comparing this with:

Comparing coefficients we get:

and

Is this equal to:

and ?

For the next part:

This gives:

and since the -2 on the LHS does not contain a t then there is no value of for which this is true.

I haven't tried it with the y's yet since it has to satisfy both these conditions to be homogeneous. Since this one doesn't work the DE is non-homogeneous.

Is that about right? - October 8th 2008, 08:42 AMChris L T521
- October 8th 2008, 01:31 PMShowcase_22
Sweet!

Thanks for your help Chris!

It was also nice to know that my 200th post was such a success! 8-)