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Show that the differential equation xy + x(1+y¹)y=0 is not exact, but becomes exact when multiplied by the integrating factor μ(x, y) = Then solve the equation. xy³ The given equation is not exact, because My which is different from N₂ = 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

Show that the differential equation xy + x(1+y¹)y=0 is not exact, but becomes exact when multiplied by the integrating factor μ(x, y) = Then solve the equation. xy³ The given equation is not exact, because My which is different from N₂ = 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

Advanced Engineering Mathematics
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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Show that the differential equation xy + x(1+y¹)y=0 is not exact, but becomes exact when multiplied by the integrating factor μ(x, y) = Then solve the equation. xy³ The given equation is not exact, because My which is different from N₂ = 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 > 0.
Transcribed Image Text:Show that the differential equation xy + x(1+y¹)y=0 is not exact, but becomes exact when multiplied by the integrating factor μ(x, y) = Then solve the equation. xy³ The given equation is not exact, because My which is different from N₂ = 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 > 0.
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