Answer to Question #316867 in Differential Equations for Sara

Question #316867

2ydx+x(x^2lny-1)dy=0

Expert's answer

$\frac{2y}{x^3}dx+\left( \ln y-\frac{1}{x^2} \right) dy=0\\d\left( -\frac{y}{x^2} \right) +\ln ydy=0\\d\left( -\frac{y}{x^2}+y\ln y-y \right) =0\\-\frac{y}{x^2}+y\ln y-y=Const$

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