Question Number 140702 by help last updated on 11/May/21
Answered by liberty last updated on 12/May/21
$$\left(\mathrm{3}\right)\:\frac{\mathrm{y}^{\cancel{\mathrm{2}}} }{\mathrm{2}}\:=−\mathrm{x}\cancel{\mathrm{y}}\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\Rightarrow\:−\frac{\mathrm{dx}}{\mathrm{x}}\:=\:\frac{\mathrm{2dy}}{\mathrm{y}} \\ $$$$\Rightarrow−\mathrm{ln}\:\mathrm{x}\:+\:\mathrm{c}\:=\:\mathrm{2ln}\:\mathrm{y}\: \\ $$$$\Rightarrow\:−\mathrm{ln}\:\mathrm{Cx}\:=\:\mathrm{ln}\:\mathrm{y}^{\mathrm{2}} \\ $$$$\Rightarrow\:\frac{\mathrm{1}}{\mathrm{Cx}}\:=\:\mathrm{y}^{\mathrm{2}} \: \\ $$