$\cfrac{{dy}}{{dx}} = (1 + {x^2})(1 + {y^2})$
$\cfrac{{dy}}{{dx}} = (1 + {x^2})(1 + {y^2})$
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.: We have, $\cfrac{{dy}}{{dx}} = (1 + {x^2})(1 + {y^2})$
$\Rightarrow \cfrac{{dy}}{{1 + {y^2}}} = (1 + {x^2})dx$
…(1)
Integrating (1) both sides,
we get
${\tan ^{ - 1}}y = x + \cfrac{1}{3}{x^3} + C$, which is the required solution.
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