Calculus, 10th Edition (Anton)

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


$$y = \tan(x^2+c) $$

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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