(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\frac{dy}{dx}=\frac{x+3y}{3x+y}[/tex]

2. Relevant equations

M(x,y)dx+N(x,y)dy=0

Exact equation (I think)

3. The attempt at a solution

Ok, so I try to put it in the form of the of an exact equation, like above, but I end up with

-(x+3y)dx+(3x+y)dy=0

This results in the partial of M with respect to y being -3 and the Partial of N with respect to x being 3, which is not equal!

I tried investigating to see if there is an integrating factor but [tex]\frac{M_{y}-N_{x}}{N}[/tex] and [tex]\frac{N_{x}-M_{y}}{M}[/tex] are not functions of just one variable. What am I doing wrong? Different method? Algebra mistake?

Thanks

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# Differential Equation

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