A) F(x,y) = (- sin(2a² – 2y), x sin(2x² – 2y)) Ty B) F(x, y) = xVy² + 1 y² + 1° C) F(x, y) = (cos(x + y) – y sin(x + y), –x sin(x + y)) 2y D) F(r. 9) = ( ) 2x x² + y² + 1' æ² + y² + 1

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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Here are four options. In each of them a vector field. Select the vector field for which path independence is guaranteed.

A) F(x,y) = (- sin(2a² – 2y), x sin(2x² – 2y))
Ty
B) F(x, y) =
xVy² + 1
y² + 1°
C) F(x, y) = (cos(x + y) – y sin(x + y), –x sin(x + y))
2y
D) F(r. 9) = ( )
2x
x² + y² + 1' æ² + y² + 1
Transcribed Image Text:A) F(x,y) = (- sin(2a² – 2y), x sin(2x² – 2y)) Ty B) F(x, y) = xVy² + 1 y² + 1° C) F(x, y) = (cos(x + y) – y sin(x + y), –x sin(x + y)) 2y D) F(r. 9) = ( ) 2x x² + y² + 1' æ² + y² + 1
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