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(²) dy.
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(²) dy.
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(y²2) dy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ea2a71-9ac4-4e85-921f-8e0d04f36029%2Fc05d052c-ba27-4f1a-9a67-f31d75c0458f%2F6zm4h6_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(y²2) dy.
Transcribed Image Text: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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