March 26th, 2011, 12:04 AM  #1 
Member Joined: Jul 2010 Posts: 34 Thanks: 0  Exact ODE
Okay so I have (2xy5x)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. 
March 26th, 2011, 12:41 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Exact ODE
5x should be 5x²/2, so the implicit solution is x²y  5x²/2 + y³/3 = C for constant C.


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