The solution of the differential equation $\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is :

Question

The solution of the differential equation

$\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is :

$\log _e|x+y|+\frac{x y}{(x+y)^2}=0$

$\log _e|x+y|-\frac{x y}{(x+y)^2}=0$

$\log _e|x+y|+\frac{2 x y}{(x+y)^2}=0$

$\log _e|x+y|-\frac{2 x y}{(x+y)^2}=0$

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