Question

The differential equation $(-xysin x + 2ycos x)dx + 2xcos xdy = 0$ is Select the correct answer. a. exact with solution $-xycos x + ysin x + 2xycos x = c$ b. exact with solution $-xycos x + ysin x + 2xycos x + c$ c. exact with solution $-2xycos x + ysin x + 2xycos x = c$ d. not exact but having an integrating factor $xy$ e. not exact but having an integrating factor $y$

          The differential equation $(-xysin x + 2ycos x)dx + 2xcos xdy = 0$ is
Select the correct answer.
a. exact with solution $-xycos x + ysin x + 2xycos x = c$
b. exact with solution $-xycos x + ysin x + 2xycos x + c$
c. exact with solution $-2xycos x + ysin x + 2xycos x = c$
d. not exact but having an integrating factor $xy$
e. not exact but having an integrating factor $y$

The differential equation (-xysin x + 2ycos x)dx + 2xcos xdy = 0 is
Select the correct answer.
a. exact with solution -xycos x + ysin x + 2xycos x = c
b. exact with solution -xycos x + ysin x + 2xycos x + c
c. exact with solution -2xycos x + ysin x + 2xycos x = c
d. not exact but having an integrating factor xy
e. not exact but having an integrating factor y

Added by Daniel W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/06/2023

Step 1

First, let's rewrite the given differential equation in the standard form: $$xysin(x)dx + (2ycos(x) - 2xcos(x))dy = 0$$ Now, let's identify the functions M(x, y) and N(x, y): $$M(x, y) = xysin(x) \quad \text{and} \quad N(x, y) = 2ycos(x) - 2xcos(x)$$ Show more…

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The differential equation (-xy sin x + 2y cos x) dx + 2x cos x dy = 0 is: a. exact with solution -xy cos x + y sin x + 2xy cos x = c b. exact with solution -xy cos x + y sin x + 2xy cos x + c c. exact with solution -2xy cos x + y sin x + 2xy cos x = c d. not exact but having an integrating factor xy e. not exact but having an integrating factor y