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I was reviewing this site and for #2, does it look like there is a typo? I am not getting that same discriminant, and a little unclear on the sketch. Can someone please explain it?

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The discriminant of the PDE $$Au_{xx}+2Bu_{xy}+Cu_{yy}=0$$ is $B^2-AC$, so I don't think there's any mistake. NB the convention in use here that the coefficient of $u_{xy}$ is written as $2B$. –  user12477 Sep 10 '12 at 8:39

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