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Q46Section II (Mathematics)46 of 84

Integrability of a Pfaffian equation: X⋅curl⁡X=0X\cdot\operatorname{curl}X=0

The Pfaffian differential equation Xˉ⋅drˉ=P(x,y,z) dx+Q(x,y,z) dy+R(x,y,z) dz=0\bar X\cdot d\bar r=P(x,y,z)\,dx+Q(x,y,z)\,dy+R(x,y,z)\,dz=0 is integrable if:

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