Word Count : 164

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From $$ \frac{dx}{y-z}=\frac{dy}{z-x}=\frac{dz}{x-y}=\lambda $$ we have the differential relations $$ dx=\lambda(y-z),\qquad dy=\lambda(z-x),\qquad dz=\lambda(x-y). $$ Adding the three equations gives $d(x+y+z)=0$, so $$ x+y+z=C_1\quad(\text{constant}). $$ Multiply the three relations by $x,y,z$ respectively and ____ ________ ____ ___ _____ _____ _________ ____ _______ __________ __________ ___.
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