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: 24

Answer

$y=x^2(2+e^x)$ is a solution to the given differential equation.

Work Step by Step

We will find $y'$ and put it into the differential equation along with $y$. $$y'= (x^2(2+e^x))'= (x^2)'(2+e^x)+x^2(2+e^x)'=2x(2+e^x)+x^2((2)'+(e^x)') = 4x+2xe^x+x^2e^x$$ Putting this into the differential equation we get The Left side: $$x(4x+2xe^x+x^2e^x)-2x^2(2+e^x) = 4x^2+2x^2e^x+x^3e^x-4x^2-2x^2e^x = x^3e^x.$$ The Right side is just $$x^3e^x.$$ We see that the Left side is equal to the Right side so $y=x^2(2+e^x)$ IS a solution to this 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.