Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 9 - Differential Equations - 9.1 Modeling with Differential Equations - 9.1 Exercises - Page 630: 2


See the proof as shown below.

Work Step by Step

Need to verify the differential equation: $t\dfrac{dy}{dt}=y+t^2 \sin t$ $t[-\cos t+ t \sin t-1] =[-t \cos t- t]+t^2 \sin t$ or, $- t \cos t +t^2 \sin t-t=-t \cos t- t+t^2 \sin t$ or, $-t \cos t- t=-t \cos t- t$ Now check the initial conditions. Since, we have $y=-t \cos t- t$ when $t =\pi$ Then $y(\pi )=-\pi \cos \pi-\pi$ or, $0=0$ Hence, it has been verified .
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