$\begin{aligned} & \frac{d y}{d x}=1+x+y^2+x y^2=(1+x)\left(1+y^2\right) \\ & \Rightarrow \int \frac{d y}{1+y^2}=\int(1+x) d x \\ & \Rightarrow \tan ^{-1} y=x+\frac{x^2}{2}+c \\ & \because y(0)=0 \Rightarrow c=0 \\ & \Rightarrow \tan ^{-1} y=x+\frac{x^2}{2} \\ & \Rightarrow y=\tan \left(x+\frac{x^2}{2}\right)\end{aligned}$