Differential equation dx/(xz-y)=dy/(yz-x)=dz/(xy-z)

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     1                dy       
----------- = -----------------
-y(x) + x*z   -dx*x + dx*z*y(x)

$$\frac{1}{x z - y{\left(x \right)}} = \frac{dy}{- dx x + dx z y{\left(x \right)}}$$

1/(x*z - y) = dy/(-dx*x + dx*z*y)

The answer [src]

       x*(dx + dy*z)
y(x) = -------------
         dy + dx*z

$$y{\left(x \right)} = \frac{x \left(dx + dy z\right)}{dx z + dy}$$

Plot the graph at C=-1

Plot the graph at C=0

Plot the graph at C=1

The classification

nth algebraic

nth algebraic Integral