Question

Solve the differential equation y'=x(1+y^2)

Answer 1

$y^{\prime}=x(1+y^2)\\ \frac{dy}{1+y^2}=x\,dx\\ \arctan(y) = \frac{x^2}{2}+C\\ y=\tan(\frac{1}{2}(x^2+C))$