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y+ (2xy-e-2y) y' = 0

y+ (2xy-e-2y) 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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Question

21

y' =0 blem ven em le is also exact. In each of Problems 15 and 16, show that the given equation is not factor. Then solve the equation. exact but becomes exact when multiplied by the given integrating 15. x2y³ + x(1+ y²) y' = 0, ation M(x) + N(y) y' = 0 u(x, y) = 1/(xy³) 16. (x + 2) sin y + (x cos y) y' = 0, p(x, y) = xe* 17. Show that if (Nx - My)/M = Q, where Q is a function of only, then the differential equation M + Ny' = 0 has an integrating factor of the form J 20. 21. 22. μ(y) = exp In each of Problems 18 through 21, find an integrating factor and solve the given equation. 1 Q(y)dy. 18. (3x2y + 2xy + y³) + (x² + y²) y' = 0 (5) 19. y'=e²x + y - 1 1+(x/y sin y) y' = 0 y+ (2xy-e-2y) y' = 0 Solve the differential equation (3xy + y²) + (x² + xy) y' = 0 alt using the integrating factor u(x, y) = (xy(2x + y))-¹. Verify that the solution is the same as that obtained in Example 4 with a different integrating factor.
Transcribed Image Text:y' =0 blem ven em le is also exact. In each of Problems 15 and 16, show that the given equation is not factor. Then solve the equation. exact but becomes exact when multiplied by the given integrating 15. x2y³ + x(1+ y²) y' = 0, ation M(x) + N(y) y' = 0 u(x, y) = 1/(xy³) 16. (x + 2) sin y + (x cos y) y' = 0, p(x, y) = xe* 17. Show that if (Nx - My)/M = Q, where Q is a function of only, then the differential equation M + Ny' = 0 has an integrating factor of the form J 20. 21. 22. μ(y) = exp In each of Problems 18 through 21, find an integrating factor and solve the given equation. 1 Q(y)dy. 18. (3x2y + 2xy + y³) + (x² + y²) y' = 0 (5) 19. y'=e²x + y - 1 1+(x/y sin y) y' = 0 y+ (2xy-e-2y) y' = 0 Solve the differential equation (3xy + y²) + (x² + xy) y' = 0 alt using the integrating factor u(x, y) = (xy(2x + y))-¹. Verify that the solution is the same as that obtained in Example 4 with a different integrating factor.
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