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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) =

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 5E
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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) =
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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