Question

Which of the following functions are solutions of the differential equation $y'' + y = \sin(x)$? (Select all that apply.) $y = \frac{1}{2}x \sin(x)$ $y = -\frac{1}{2}x \cos(x)$ $y = x \sin(x) - 4x \cos(x)$ $y = \sin(x)$ $y = \cos(x)$

Name: which of the following functions are solutions of the differential equation y y sinx select all that apply y frac12x sinx y frac12x cosx y x sinx 4x cosx y sinx y cosx 22044
Uploaded: 2022-12-06T17:22:58-08:00
Duration: 1 min 56 s
Channel: Sri K
Description: which of the following functions are solutions of the differential equation y y sinx select all that apply y frac12x sinx y frac12x cosx y x sinx 4x cosx y sinx y cosx 22044

          Which of the following functions are solutions of the differential equation $y'' + y = \sin(x)$? (Select all that apply.)
$y = \frac{1}{2}x \sin(x)$
$y = -\frac{1}{2}x \cos(x)$
$y = x \sin(x) - 4x \cos(x)$
$y = \sin(x)$
$y = \cos(x)$

$which of the following functions are solutions of the differential equation y y sinx select all that apply y frac12x sinx y frac12x cosx y x sinx 4x cosx y sinx y cosx 22044$

Added by Kristina H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

12/06/2022

Step 1

To do this, we need to calculate the first and second derivatives of each given function and then substitute them into the differential equation to check if the equation holds true. The differential equation is $y'' + y = \sin(x)$. Let's check each Show more…

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Which of the following functions are solutions of the differential equation $y'' + y = \sin(x)$? (Select all that apply.) $y = \frac{1}{2}x \sin(x)$ $y = -\frac{1}{2}x \cos(x)$ $y = x \sin(x) - 4x \cos(x)$ $y = \sin(x)$ $y = \cos(x)$