Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 10 - Introduction to Differential Equations - 10.1 Solving Differential Equations - Exercises - Page 505: 30


$$x =\sin ^{-1}\left(C e^{t / 2}\right) $$

Work Step by Step

\begin{aligned} \frac{dx}{dt}&=t\tan t\\ \cot x d x &=t d t \\ \int \cot x d x &=\int t d t \\ \ln \sin x &=\frac{t^{2}}{2}+\ln C \\ \sin x &=C e^{t^{2} / 2} \\ x &=\sin ^{-1}\left(C e^{t / 2}\right) \end{aligned}
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