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b) Use the result in item (a) to determine whether there is a function y, and z such that ox(x, y, z) = x + y + 5z, Øy(x, y, z) = 4x – 2y², and of three variables x, z(x, y, z) = 2³ – 3y.

b) Use the result in item (a) to determine whether there is a function y, and z such that ox(x, y, z) = x + y + 5z, Øy(x, y, z) = 4x – 2y², and of three variables x, z(x, y, z) = 2³ – 3y.

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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Answer subproblem b. The solution to subproblem a wherein the divergence and curl is determined is also attached below.

(a) Find the divergence and curl of the vector field Ğ(x, y, z) = (x + y + 5z, 4x − 2y², 2³ – 3y). (b) Use the result in item (a) to determine whether there is a function of three variables x, y, and z such that ox(x, y, z) = x + y + 5z, Oy(x, y, z) = 4x – 2y², and z(x, y, z) = 2³ – 3y.
Transcribed Image Text:(a) Find the divergence and curl of the vector field Ğ(x, y, z) = (x + y + 5z, 4x − 2y², 2³ – 3y). (b) Use the result in item (a) to determine whether there is a function of three variables x, y, and z such that ox(x, y, z) = x + y + 5z, Oy(x, y, z) = 4x – 2y², and z(x, y, z) = 2³ – 3y.
O Step 2 Divergence is, 7. G = 2(x+y+52) + D_ (4x-2y ²) + 0 (2 ²34) = 1-4y +37? 1-47+372 So the Divergence is 1-4y+37? Step 3 Compute :- 2234 1 x+y +57 4x-24 = 2 ( 21 (2 ² 38) _ B (47-24³7) - ( 2 (2 ²34) - D₂ (2+y+52)) J. + ^ ( 37 (1x2-24²) - By (x+y₁52)) = -30 +51 +3×. Therefore Curl is. VxG = -31+50 +34.
Transcribed Image Text:O Step 2 Divergence is, 7. G = 2(x+y+52) + D_ (4x-2y ²) + 0 (2 ²34) = 1-4y +37? 1-47+372 So the Divergence is 1-4y+37? Step 3 Compute :- 2234 1 x+y +57 4x-24 = 2 ( 21 (2 ² 38) _ B (47-24³7) - ( 2 (2 ²34) - D₂ (2+y+52)) J. + ^ ( 37 (1x2-24²) - By (x+y₁52)) = -30 +51 +3×. Therefore Curl is. VxG = -31+50 +34.
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