Question
The Pfaffian equation is integrable.
Answer :
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Let the Pfaffian equation be [ (2xy^2+2xy+2xz^2+1),dx+dy+2z,dz=0. ] Write it as [ dy+2z,dz+\bigl[2x(y^2+y+z^2)+1\bigr]dx=0. ] Observe that [ d(y+z^2)=dy+2z,dz, ] and set [ u=y+z^2. ] Then (y^2+y+z^2=u^2-u), and the
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