I am having problem solving this problem. Kind of stuck. Help would be veryy appreciated.

the problem is :

The differential equation y' = x^2 - y^2 -1 has y = -x as one of its solutions find the another solution.

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- June 30th 2009, 05:00 PM #1

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- June 30th 2009, 06:18 PM #2

- June 30th 2009, 06:58 PM #3

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i used one of the solution and

i let y = u - x

therefore y' = u'-1

plug it back into the equation and i got

u'-1 = x^2 - ( u-x)^2 -1

u'-1 = x^2 - (u^2-2ux+x^2)-1

u'-1 = x^2 - u^2 + 2ux - x^2 -1

u' = -u^2+2ux

u' = u(-u+2x)

I dunno if i am doing it correctly or not... i am stuck at the integration part

- June 30th 2009, 07:23 PM #4

- June 30th 2009, 08:48 PM #5

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- June 30th 2009, 09:30 PM #6

- June 30th 2009, 09:33 PM #7

- July 1st 2009, 01:58 AM #8

- July 1st 2009, 03:02 AM #9

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