Solve the following differential equation: `y^2dx+(x^2-x y+y^2)dy=0`

Explanation

$$ \begin{aligned} &\mathrm{y}^{2} \mathrm{dx}+\left(\mathrm{x}^{2}-\mathrm{xy}+\mathrm{y}^{2}\right) \mathrm{dy}=0 \\ &\Rightarrow \quad y^{2} d x=-\left(x^{2}-x y_{4}+y^{2}\right) d y \\ &\Rightarrow \quad y^{2} \frac{d x}{d y}=-\left(x^{2}-x y+y^{2}\right) \\ &\Rightarrow \quad \frac{d x}{d y}=-\left(\frac{x^{2}}{y^{2}}-\frac{x}{y}+1\right) \end{aligned} $$
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