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> $$x^2dy-y^2dx+xy^2(x-y)dy=0$$
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What I tried:
$$\frac{x^2}{y^2} \frac{dy}{dx}+x(x-y)\frac{dy}{dx}=1\\$$
Let $h=-1/x, \; k=-1/y,\; dh=1/x^2 \, dx, \; dk=1/y^2 \,dy$
$$\frac{dk}{dh}+\frac{(k-h)}{k^2} \frac{dk}{dh}=1\\
\frac{dk}{dh}+\frac hk=1+\frac1k\\
he^{\int-1/k^2\; dk}=\int\left(1+\frac1k\right)e^{\int-1/k^2\; dk}dk\\
he^{-y}=\int\frac{1-y}{y^2}e^{-y}dy=\int\left(\frac 1{y^2}-\frac1y\right)e^{-y}dy$$
Which probably is unsolvable?I tried using IBP on RHS.**Dont use Ricatti Eqn(Not in my course)**
Answer is:

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>  $$\large\ln\left|\frac{x-y}{xy}\right|=\frac{y^2}2+\mathcal C$$
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