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
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
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.
Find the potential function U(x, y) subject to the condition U(0, 0) = 5 in the case of the total
differential.
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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