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Show that the differential equation x¹y³ + x(1+y¹)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor Then solve the equation. μ(x, y) = 1 xy5*

Show that the differential equation x¹y³ + x(1+y¹)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor Then solve the equation. μ(x, y) = 1 xy5*

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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Show that the differential equation x¹y³ + x(1+y¹)y' = 0_ is not exact, but becomes exact when multiplied by the integrating factor Then solve the equation. μ(x, y) = 1 xy5* The given equation is not exact, because My : which is different from N = 1+y4 0 5 x² y After multiplication with u(x, y), the equation is exact, because then My = N₂ = - The general solution of the differential equation is given implicitly by = c, for any constant c, where y +04 In y
Transcribed Image Text:Show that the differential equation x¹y³ + x(1+y¹)y' = 0_ is not exact, but becomes exact when multiplied by the integrating factor Then solve the equation. μ(x, y) = 1 xy5* The given equation is not exact, because My : which is different from N = 1+y4 0 5 x² y After multiplication with u(x, y), the equation is exact, because then My = N₂ = - The general solution of the differential equation is given implicitly by = c, for any constant c, where y +04 In y
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