Differential Equations — Class 12 Maths Solution

.: 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.