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*}
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 8 - Mathematical Modeling With Differential Equations - 8.2 Separation Of Variables - Exercises Set 8.2 - Page 575: 2
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