In this problem we consider an equation in differential form M dx + N dy = 0. The equation (6x + 4x'y²) dx + (6x² - + 3)dy = 0 in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have M, - N, = For this exercise we can find an integrating factor which is a function of y alone since M, - N, is a function of y alone. Namely we have (y) = Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where M = N = Which is exact since M, N = are equal. This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where F(x, y) =
In this problem we consider an equation in differential form M dx + N dy = 0. The equation (6x + 4x'y²) dx + (6x² - + 3)dy = 0 in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have M, - N, = For this exercise we can find an integrating factor which is a function of y alone since M, - N, is a function of y alone. Namely we have (y) = Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where M = N = Which is exact since M, N = are equal. This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where F(x, y) =
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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Transcribed Image Text:In this problem we consider an equation in differential form M dx + N dy = 0.
The equation
(6x + 4x'y2) dx + (6x² - + 3)dy = 0
y
in differential form M dx + Ñ dy = 0 is not exact. Indeed, we have
M, - N, =
For this exercise we can find an integrating factor which is a function of y alone since
M,- N,
M
is a function of y alone.
Namely we have u(y) =|
Multiplying the original equation by the integrating factor we obtain a new equation M dx + N dy = 0 where
M =
N =
Which is exact since
M, =
N =
are equal.
This problem is exact. Therefore an implicit general solution can be written in the form F(x, y) = C where
F(x, y) =
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