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Exact equationsby TheFirstOrder
Tags: eaxt equations 
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#1
Mar1410, 03:00 AM

P: 3

1. The problem statement, all variables and given/known data
Solve ((y^2)+xy+1)dx+((x^2)+xy+1)dy=0 using the method of exact equations. 2. Relevant equations I must use: (N[tex]_{x}[/tex]M[tex]_{y}[/tex])/(xMyN)=F(xy) 3. The attempt at a solution The problem that I'm having is that I can't get the required partial derivatives to be equal to each other. How do can I change it so that N[tex]_{x}[/tex]=M[tex]_{y}[/tex]? When I started this problem initially, I got F(xy)=1, which is not right as 1 is not a function of xy (and I had forgotten to check that the partial derivatives were equal to each other) :P Please help. It's my first time here. And sorry, the superscripts are meant to be subscripts! 


#2
Mar1410, 03:21 AM

HW Helper
P: 2,322

Since Nx is not equal to My, the equation isn't exact. Are you sure you copied the question correctly?



#3
Mar1410, 03:26 AM

P: 3

Mx=2y+x Ny=2x+y I read things in my textbook that says I could times the original equation by a factor that would result in the two partial equations being equal, but that doesn't seem to work in this case. I'm completely clueless. 


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