The solution of the D.E {1x−y2(x−y)2}dx+{x2(x−y)2−1y}dy=0 (Where C is the parameter)

(dxx−dyy)+dyy2−dxx2(1y−1x)2=0 dxx−dyy+d(11y−1x)=0Integrating log|x|−log|y|+11y−1x=C log|xy|+xyx−y=c

The solution of the D.E {1x−y2(x−y)2}dx+{x2(x−y)2−1y}dy=0 (Where C is the parameter)

(dxx−dyy)+dyy2−dxx2(1y−1x)2=0 dxx−dyy+d(11y−1x)=0Integrating log|x|−log|y|+11y−1x=C log|xy|+xyx−y=c

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The solution of the D.E ${\frac{1}{x} - \frac{y^{2}}{{(x - y)}^{2}}} d x + {\frac{x^{2}}{{(x - y)}^{2}} - \frac{1}{y}} d y = 0$ (Where C is the parameter)

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$\frac{x y}{x - y} = c e^{x / y}$

$\ln | x y | = c + \frac{x y}{x - y}$

$\ln | x y | = c + \frac{2 x y}{x - y}$

$\ln | \frac{x}{y} | + \frac{x y}{x - y} = c$

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$(\frac{d x}{x} - \frac{d y}{y}) + \frac{\frac{d y}{y^{2}} - \frac{d x}{x^{2}}}{{(\frac{1}{y} - \frac{1}{x})}^{2}} = 0 \frac{d x}{x} - \frac{d y}{y} + d (\frac{1}{\frac{1}{y} - \frac{1}{x}}) = 0$

Integrating

$\log | x | - \log | y | + \frac{1}{\frac{1}{y} - \frac{1}{x}} = C \log | \frac{x}{y} | + \frac{x y}{x - y} = c$

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The solution of the D.E {1x−y2(x−y)2}dx+{x2(x−y)2−1y}dy=0 (Where C is the parameter)

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The solution of the D.E ${\frac{1}{x} - \frac{y^{2}}{{(x - y)}^{2}}} d x + {\frac{x^{2}}{{(x - y)}^{2}} - \frac{1}{y}} d y = 0$ (Where C is the parameter)