Chapter 2. First Order Differential Equations 24. Show that if (N - M)/M-yN) R, where R depends on the quantity xy only, then the differential equation has an integrating factor of the form uxy). Fin a general formula for this integrating factor In each of Problems 25 through 31,find an integrating factor and solve the given equation 25. (3x2y + 2xy + y*) + (x2 + y2)y' 0 27. 1 + (x/y-siny)y' -0 29. er + (ex coty-2ycscy)y' = 0 28, y + (2xy-e-2y)y' = 0 0 Hint: See Problem 24. 32. Solve the differential equation using the integrating factor u(r, y) [xy2x +y)l-1. Verify that the solution is the sa as that obtained in Example 4 with a different integrating factor. merical Approximations: Euler's Method
Chapter 2. First Order Differential Equations 24. Show that if (N - M)/M-yN) R, where R depends on the quantity xy only, then the differential equation has an integrating factor of the form uxy). Fin a general formula for this integrating factor In each of Problems 25 through 31,find an integrating factor and solve the given equation 25. (3x2y + 2xy + y*) + (x2 + y2)y' 0 27. 1 + (x/y-siny)y' -0 29. er + (ex coty-2ycscy)y' = 0 28, y + (2xy-e-2y)y' = 0 0 Hint: See Problem 24. 32. Solve the differential equation using the integrating factor u(r, y) [xy2x +y)l-1. Verify that the solution is the sa as that obtained in Example 4 with a different integrating factor. merical Approximations: Euler's Method
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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