need your help on this...

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

Answer: x^2 + y^2 = cy

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- Jul 15th 2009, 03:43 PMredfox2600Exact Differential Equation
need your help on this...

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

Answer: x^2 + y^2 = cy - Jul 15th 2009, 03:51 PMKrizalid
It's also homogeneous, or you do need to solve it as a exact one?

- Jul 15th 2009, 04:12 PMRandom Variable
That's not an exact equation unless it's $\displaystyle -2xydx +(y^{2}-x^{2}) dy =0 $ or $\displaystyle 2xydx +(y^{2}+x^{2}) dy =0 $

- Jul 15th 2009, 05:15 PMredfox2600
thanks.

you're right, it's homogeneous.

a little need help please.

i'm stuck in the ending part.

how come that c has a y ( cy )ln |y| + ln |v^2 + 1| = c

thanks. - Jul 15th 2009, 05:30 PMKrizalid
- Jul 16th 2009, 03:29 PMredfox2600
thanks for big help Krizalid.

- Jul 22nd 2009, 01:20 AMdefog171
the ODE is not exact, so you should find an "intergrating factor" to multiply with the original ODE so that the NEW ODE is solvable. R u interested on how to solve the problem?

- Jul 24th 2009, 03:06 PMredfox2600
yes. thanks for the great help.