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: 36

Answer

$y=\frac{x^{n+2}}{(n+1)(n+2)}+C_1x+C_2$, 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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.