Word Count : 204

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Consider the Pfaffian form (M,dx+N,dy+P,dz=0) with (M=yz,; N=x^{2}y-zx,; P=x^{2}z-xy). The condition for integrability is (M\left(\frac{\partial N}{\partial z}-\frac{\partial P}{\partial y}\right)+N\left(\frac{\partial P}{\partial x}-\frac{\partial M}{\partial z}\right)+P\left(\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}\right)=0). Now (\frac{\partial N}{\partial z}=-x,; \frac{\partial P}{\partial y}=-x), hence the first bracket is zero. (\frac{\partial P}{\partial x}=2xz-y,; \frac{\partial M}{\partial z}=y), so (\frac{\partial P}{\partial x}-\frac{\partial M}{\partial __________ ________ ______ ___ _____ __________ ___ _______ ______ ____ __________ ________.
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