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The differential equation M(x, y)dx + N(x, y)dy = 0 is called an exact equation if continuous function u(x, y) such that du = M(x, y)dx + N (x, y)dy exists. Prove that the following %3D equation are exact. Then, solve the equations. a) (6x? + 10xy – 3y?)dx + (5x2 – 6xy + 3y?)dy = 0. b) (cos x – x sin x + y?)dx + 2xy dy = 0

The differential equation M(x, y)dx + N(x, y)dy = 0 is called an exact equation if continuous function u(x, y) such that du = M(x, y)dx + N (x, y)dy exists. Prove that the following %3D equation are exact. Then, solve the equations. a) (6x? + 10xy – 3y?)dx + (5x2 – 6xy + 3y?)dy = 0. b) (cos x – x sin x + y?)dx + 2xy dy = 0

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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The differential equation M(x, y)dx + N(x, y)dy = 0 is called an exact equation if continuous function u(x, y) such that du = M(x,y)dx + N (x, y)dy exists. Prove that the following equation are exact. Then, solve the equations. a) (6x2 + 10xy – 3y?)dx + (5x2 – 6xy + 3y2)dy = 0. b) (cos x – x sin x + y?)dx + 2xy dy = 0
Transcribed Image Text:The differential equation M(x, y)dx + N(x, y)dy = 0 is called an exact equation if continuous function u(x, y) such that du = M(x,y)dx + N (x, y)dy exists. Prove that the following equation are exact. Then, solve the equations. a) (6x2 + 10xy – 3y?)dx + (5x2 – 6xy + 3y2)dy = 0. b) (cos x – x sin x + y?)dx + 2xy dy = 0
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