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For the slope field shown, which could be a family of anti-derivatives? y -6.28 6.28 O y = – cos x + C O y =x + C o y = sin x + C O y =x + C /// //// /// // /// // / // // // /// ///

For the slope field shown, which could be a family of anti-derivatives? y -6.28 6.28 O y = – cos x + C O y =x + C o y = sin x + C O y =x + C /// //// /// // /// // / // // // /// ///

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For the slope field shown, which could be a family of anti-derivatives? y -6.28 6.28 оу%3 — соS х + C | O y = x + C o y= sin x + C O y = x + C /// / { /// // /// // /// /// ///// //// /////
Transcribed Image Text:For the slope field shown, which could be a family of anti-derivatives? y -6.28 6.28 оу%3 — соS х + C | O y = x + C o y= sin x + C O y = x + C /// / { /// // /// // /// /// ///// //// /////
Expert Solution
Step 1

Given slop field is

Advanced Math homework question answer, step 1, image 1

Now we check all options one by one.

 

option 1:

Given

y=-cos(x)+C

Differentiating, we get

y'=cox

So, slop field for above is

Advanced Math homework question answer, step 1, image 2

 

option 2:

Given

y=x2+c⇒y'=2x

So, slop field is

Advanced Math homework question answer, step 1, image 3

 

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