Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 1 - First-Order Differential Equations - 1.2 Basic Ideas and Terminology - Problems - Page 22: 34

Answer

$y'=x^{-2/3}$$ $$y=3x^{1/2}+C$, valid for all real values

Work Step by Step

Integrate the function to turn $y'$ into $y$. Use power rule and don't forget an integration constant. $$y'=x^{-2/3}$$ $$y=3x^{1/2}+C$$ This solution is valid for all real values.
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