Solve $ x(x^2-y^2-z^2)dx-2xydy+2xz=0$ using Lagrange multipliers. I was able to find only one solution by making use of the last two fractions in Lagrange auxiliary equations.
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1Please. Show your efforts. – Cesareo Sep 22 '20 at 09:54
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Taking last two fractions of Lagrange auxilary equations $\frac{dy}{-2xy}=\frac{dz}{-2xz}$, we can find one solution as $y=cz$, for some constant $c$. I could not able to find any set of multipliers to find another solutions – Rag Sep 22 '20 at 13:08