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if-z-z-2-3x-xy-0-show-that-d-2-z-dx-2-d-2-z-dy-2-2x-x-1-z-2-3-3-




Question Number 182949 by akolade last updated on 17/Dec/22
if z(z^2 +3x)+xy=0 show that  (d^2 z/dx^2 )+(d^2 z/dy^2 ) = ((2x(x−1))/((z^2 +3)^3 ))
$$\mathrm{if}\:\mathrm{z}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3x}\right)+\mathrm{xy}=\mathrm{0}\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{z}}{\mathrm{dx}^{\mathrm{2}} }+\frac{\mathrm{d}^{\mathrm{2}} \mathrm{z}}{\mathrm{dy}^{\mathrm{2}} }\:=\:\frac{\mathrm{2x}\left(\mathrm{x}−\mathrm{1}\right)}{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{3}} } \\ $$

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