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: 36


$y=\frac{x^{n+2}}{(n+1)(n+2)}+C_1x+C_2$, valid for all values.

Work Step by Step

Integrate the function to turn $y''$ into $y'$. Don't forget integration constants. $$y''=x^n$$ $$y'=\frac{x^{n+1}}{n+1}+C_1$$ Integrate once again to turn $y'$ to $y$. $$y=\frac{x^{n+2}}{(n+1)(n+2)}+C_1x+C_2$$ This solution is valid for all values.
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