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Show that the differential equation_xºy7 +x(1+yº)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor μ(x, y) = 1 xy7 Then solve the equation. The given equation is not exact, because My 6 = 7 x y which is different from N = 1+y6 After multiplication with u(x, y), the equation is exact, because then My N = 0 The general solution of the differential equation is given implicitly by x6 1 6 6 y6 c, for any constant c, here y > 0.

Show that the differential equation_xºy7 +x(1+yº)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor μ(x, y) = 1 xy7 Then solve the equation. The given equation is not exact, because My 6 = 7 x y which is different from N = 1+y6 After multiplication with u(x, y), the equation is exact, because then My N = 0 The general solution of the differential equation is given implicitly by x6 1 6 6 y6 c, for any constant c, here y > 0.

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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Your answer is partially correct. Show that the differential equation_x³y² + x(1+yº)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor 1 μ(x, y) Then solve the equation. = xy7 The given equation is not exact, because My 7 x6 yo ✓ which is different from N 1+y = After multiplication with u(x, y), the equation is exact, because then My = N =10 The general solution of the differential equation is given implicitly by x6 1 C₂ for any constant c, where y > 0. 6 6 y6 Edit
Transcribed Image Text:Your answer is partially correct. Show that the differential equation_x³y² + x(1+yº)y' = 0 is not exact, but becomes exact when multiplied by the integrating factor 1 μ(x, y) Then solve the equation. = xy7 The given equation is not exact, because My 7 x6 yo ✓ which is different from N 1+y = After multiplication with u(x, y), the equation is exact, because then My = N =10 The general solution of the differential equation is given implicitly by x6 1 C₂ for any constant c, where y > 0. 6 6 y6 Edit
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