Determine which of the differentials (or both) is the total differential: a) 2[cos(2x+2y²) + x ] dx − [4y sin(2x + 2y²) + 1] dy; b) 6 sin(y) e²x+dx + 3(siny+cosy)e²x+y-2 y sin(v²) dy. Find the potential function U(x, y) subject to the condition U(0, 0) = 5 in the case of the total differential.
Determine which of the differentials (or both) is the total differential: a) 2[cos(2x+2y²) + x ] dx − [4y sin(2x + 2y²) + 1] dy; b) 6 sin(y) e²x+dx + 3(siny+cosy)e²x+y-2 y sin(v²) dy. Find the potential function U(x, y) subject to the condition U(0, 0) = 5 in the case of the total differential.
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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![Determine which of the differentials (or both) is the total differential:
a) 2[cos(2x+2y²) + x ] dx − [4y sin(2x + 2y²) + 1] dy;
b) 6 sin(y) e²x+dx + 3(siny+cosy)e²x+y-2 y sin(v²) dy.
Find the potential function U(x, y) subject to the condition U(0, 0) = 5 in the case of the total
differential.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55521067-0384-497f-95f8-f51a06d5dbdf%2F8073d425-9b95-47c6-939c-691a2663c046%2Fujmi9sf_processed.png&w=3840&q=75)
Transcribed Image Text:Determine which of the differentials (or both) is the total differential:
a) 2[cos(2x+2y²) + x ] dx − [4y sin(2x + 2y²) + 1] dy;
b) 6 sin(y) e²x+dx + 3(siny+cosy)e²x+y-2 y sin(v²) dy.
Find the potential function U(x, y) subject to the condition U(0, 0) = 5 in the case of the total
differential.
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