M, - N, - this exercise we can find an integrating factor which is a function of x alone since My un be considered as a function of x alone. amely we have u(x)= Multiplying the original equation by the integrating factor we obtain a new equation M da + N dy = 0 where M N = %3D Which is exact since My

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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Question
The equation
(2ye2 -8) dæ + (e²" (2x + 3y²))dy = 0
in differential form M dx + N dy = 0 is not exact. Indeed, we have
My- N2
I
For this exercise we can find an integrating factor which is a function of x alone since
M,- N2
can be considered as a function of a alone.
Namely we have µ(x)
Multiplying the original equation by the integrating factor we obtain a new equation
M da + N dy = 0 where
%3D
M =
N =
Which is exact since
My
Transcribed Image Text:The equation (2ye2 -8) dæ + (e²" (2x + 3y²))dy = 0 in differential form M dx + N dy = 0 is not exact. Indeed, we have My- N2 I For this exercise we can find an integrating factor which is a function of x alone since M,- N2 can be considered as a function of a alone. Namely we have µ(x) Multiplying the original equation by the integrating factor we obtain a new equation M da + N dy = 0 where %3D M = N = Which is exact since My
Multiplying the original equation by the integrating factor we obtain a new equation
M da + N dy =0 where
M%3=
N =
Which is exact since
My=
N =
are equal.
This problem is exact. Therefore an implicit geieral solution can be written in the form
F(r, y) = C where
F(x, y) D
Transcribed Image Text:Multiplying the original equation by the integrating factor we obtain a new equation M da + N dy =0 where M%3= N = Which is exact since My= N = are equal. This problem is exact. Therefore an implicit geieral solution can be written in the form F(r, y) = C where F(x, y) D
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