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Linear Equation in 2 Variables

The solution ...

Question

The solution of $x^{2} d y - y^{d} x + x y^{2} (x - y) d y = 0$ is

∣ ∣ ∣ \frac{x - y}{x y} ∣ ∣ ∣ = \frac{y^{2}}{2} + c

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∣ ∣ ∣ \frac{x y}{x - y} ∣ ∣ ∣ = \frac{x^{2}}{2} + c

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∣ ∣ ∣ \frac{x - y}{x y} ∣ ∣ ∣ = \frac{x^{2}}{2} + c

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∣ ∣ ∣ \frac{x - y}{x y} ∣ ∣ ∣ = y + c

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The solution of x2dy−ydx+xy2(x−y)dy=0 is