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: 35

Answer

See answer below

Work Step by Step

Integrate the function to turn $y′'$ into $y$. Use power rule and don't forget an integration constant. $$y''=xe^xdx$$ $$y'=xe^x-e^x+c_1$$ Integrate once again to turn y′ to y. $$y=xe^x-2e^x+c_1x+c_2=e^x(x-2)+c_1x+c_2$$ This solution is valid for all real values in $(-\infty,+\infty)$
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