Answer
$$y = \tan(x^2+c) $$
Work Step by Step
Given $$\frac{dy}{dx}=2(1+y^2)x $$
Separate variables
\begin{align*}
\int \frac{dy}{1+y^2}&=2\int x dx \\
\tan^{-1} y&=x^2+c\\
y&= \tan(x^2+c)
\end{align*}
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