Solution Found!
s M(x, y) and N(x, y) can be found so that each
Chapter 2, Problem 42E(choose chapter or problem)
Discuss how the functions M(x, y) and N(x, y) can be found so that each differential equation is exact. Carry out your ideas.
(a) \(M(x, y) \ d x+\left(x e^{x y}+2 x y+\frac{1}{x}\right) \ d y=0\)
(b) \(\left(x^{-1 / 2} y^{1 / 2}+\frac{x}{x^{2}+y}\right) \ d x+N(x, y) \ d y=0\)
Text Transcription:
M(x, y) dx + (xe^xy + 2xy + 1/x) dy = 0
(x^-1/2 y^1/2 + x/x^2 + y) dx + N(x, y) dy = 0
Questions & Answers
QUESTION:
Discuss how the functions M(x, y) and N(x, y) can be found so that each differential equation is exact. Carry out your ideas.
(a) \(M(x, y) \ d x+\left(x e^{x y}+2 x y+\frac{1}{x}\right) \ d y=0\)
(b) \(\left(x^{-1 / 2} y^{1 / 2}+\frac{x}{x^{2}+y}\right) \ d x+N(x, y) \ d y=0\)
Text Transcription:
M(x, y) dx + (xe^xy + 2xy + 1/x) dy = 0
(x^-1/2 y^1/2 + x/x^2 + y) dx + N(x, y) dy = 0
ANSWER:Step 1 of 3
In this problem we have to discuss how the functions M(x, y) and N(x, y) can be found.