The solution of the differential equation $\frac{dy}{dx}=1+x+y^2+xy^2$ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\tan^{-1}y=x+\frac{x^2}{2}+C$
$\frac{dy}{dx}=(1+x)+y^2+(1+x)=(1+y^2)(1+x)$
so $\int\frac{1}{1+y^2}dy=\int 1+x\,dx$
$\tan^{-1}y=\frac{x^2}{2}+x+C$