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March 26th, 2011, 01:04 AM   #1
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Exact ODE

Okay so I have (2xy-5x)dx + (x^2+y^2)dy = 0
u = integral of M(x,y) dx + f(y)
=yx^2 - 5x + f(y)
du/dy= N(x,y) = x^2 + y^2 and also deriving the u term = du/dy = x^2 + f'(y)
so if x^2 + y^2 = x^2 + f'(y)
Then f'(y) = y^2
and f(y) = y^3/3
so the implicit solution is yx^2 - 5x + y^3/3.
Can someone please confirm or deny this solution as my study partner and I are divided.
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March 26th, 2011, 01:41 AM   #2
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Re: Exact ODE

-5x should be -5x/2, so the implicit solution is xy - 5x/2 + y/3 = C for constant C.
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