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

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Solution

$\begin{matrix} \frac{d y}{d x} = (1 + x^{2}) (1 + y^{2}) \frac{d y}{1 + y^{2}} = (1 + x^{2}) d x I n t e g r a t e b o t h s i d e s \int \frac{1}{1 + y^{2}} d y = \int (1 + x^{2}) d x {tan}^{- 1} y = \frac{x^{3}}{3} + x + C \end{matrix}$

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