Solve: (x² - yx²) dy + (y² + xy²) dx = 0

$x^2(1 - y)\,dy + y^2(1 + x)\,dx = 0$ Separating the variables: $\frac{1-y}{y^2}\,dy + \frac{1+x}{x^2}\,dx = 0$ $\int\left(\frac{1}{y^2} - \frac{1}{y}\right)dy + \int\left(\frac{1}{x^2} + \frac{1}{x}\right)dx = C$ $-\frac{1}{y} - \log|y| - \frac{1}{x} + \log|x| = C$ Hence $\log\left|\frac{x}{y}\right| = \frac{1}{x} + \frac{1}{y} + C$.