Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 6 - Differential Equations - 6.1 Exercises: 26

Answer

$y=\cos x$ is not a solution to the given differential equation.

Work Step by Step

We will find $y'$ and substitute it along with $y$ into the given differential equation. $$y'=(\cos x)' = -\sin x.$$ Now by substituting we get: The Left side: $$xy'-2y=-x\sin x-2\cos x$$ The Right side is just $$x^3e^x.$$ The Left side is NOT equal to the right side for every $x$ so $y=\cos x$ is not a solution to the given differential equation.
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.