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 - Page 403: 22


$y=x^3$ is not a solution to given differential equation.

Work Step by Step

We will find $y'$ and put it into the given differential equation along with $y$. $$y'= (x^3)'=3x^2.$$ Putting this into the differential equation we get The Left side: $$xy'-2y= x\times 3x^2 -2x^3= 3x^3-2x^3=x^3.$$ The Right side: $$x^3e^x.$$ We see that The Left side is NOT equal to the Right side for all $x$ so $y=x^3$ is not a solution to this differential equation.
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