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#1 2007-05-20 13:04:14

Old_Steve
Member
Registered: 2007-05-15
Posts: 17

Non-Linear Diff. Eq. - Help!

It seems they make all the examples in the books easy.  Here is a first order diff. eq that I need to solve:

(3y^2 + 2xy)dx - (2xy+x^2)dy = 0

I appreciate any help!

Answer is (y^2/x^3)+(y/x^2)=c but I can't seem to get there.

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#2 2007-05-20 16:00:51

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Non-Linear Diff. Eq. - Help!

you can make it

Last edited by Stanley_Marsh (2007-05-20 16:15:06)


Numbers are the essence of the Universe

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#3 2007-05-20 22:03:51

Old_Steve
Member
Registered: 2007-05-15
Posts: 17

Re: Non-Linear Diff. Eq. - Help!

Thanks!  I had more problems with the algeraic conversion at line 2 than anything.

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#4 2007-05-21 10:18:34

Old_Steve
Member
Registered: 2007-05-15
Posts: 17

Re: Non-Linear Diff. Eq. - Help!

Can you tell me why C must be ln(C) at the end?  Why when you integrate is it not just + C?

I have other problems I am working that will only work when C = ln(C)

Last edited by Old_Steve (2007-05-21 10:19:24)

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#5 2007-05-21 11:00:19

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Non-Linear Diff. Eq. - Help!

It's just made that way to make the problem easier. C and ln C are just constants. The values of C are different, but C is arbitrary so it doesn't matter.

If it helps you understand, you could write +C in the integration step and then change that to +ln A in the next step, where A is a constant.


Why did the vector cross the road?
It wanted to be normal.

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#6 2007-05-21 13:07:04

Old_Steve
Member
Registered: 2007-05-15
Posts: 17

Re: Non-Linear Diff. Eq. - Help!

Thanks for explaining.

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