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7. (х? + 1) dy = xy? +x — ху? %3D dx

7. (х? + 1) dy = xy? +x — ху? %3D dx

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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First Order Ordinary Differential Equation 124 Chapter 3 EXERCISES 3.2 In Exercises 1-4, determine if the differential equation is separable. 1. y' = x cos y +2xy2 2. 3xy? dx – 6 sin y dy = 0 dy 16. ye dy 17. a) Sol- for %3D b) Use 3. dx = x² + 2xy 4. sin xy' = xy + 4x of pro Solve the differential equations in Exercises 5-12. 18. a) So 5. y' = 2x?y - 4y 6. e* y dx+4y³ dy = 0 for 7. (x² + 1) dy = xy? + x b) U- %3D dx of 8. sec xy'- xy/(y + 4) = 0 9. e* (y² – 4y) dx + 4 dy = 0 pi 19. Use dy x²y³ +3xy³3 dy 11. t dt dy = te dt 10. dx age) 2x?y 20. Use dr =r sin 0 de 12. (r2 + 1) cos 0 age) 21. a) S Solve the initial value problems in Exercises 13-16. 13. y' + x /y = 0, y(0) = 1 %3D b) dy 14. 3 = 2xy- y, y(2) = 1 dx dy 15. 4ху %3D dx y2 +4 (1) = 1 c) 33
Transcribed Image Text:First Order Ordinary Differential Equation 124 Chapter 3 EXERCISES 3.2 In Exercises 1-4, determine if the differential equation is separable. 1. y' = x cos y +2xy2 2. 3xy? dx – 6 sin y dy = 0 dy 16. ye dy 17. a) Sol- for %3D b) Use 3. dx = x² + 2xy 4. sin xy' = xy + 4x of pro Solve the differential equations in Exercises 5-12. 18. a) So 5. y' = 2x?y - 4y 6. e* y dx+4y³ dy = 0 for 7. (x² + 1) dy = xy? + x b) U- %3D dx of 8. sec xy'- xy/(y + 4) = 0 9. e* (y² – 4y) dx + 4 dy = 0 pi 19. Use dy x²y³ +3xy³3 dy 11. t dt dy = te dt 10. dx age) 2x?y 20. Use dr =r sin 0 de 12. (r2 + 1) cos 0 age) 21. a) S Solve the initial value problems in Exercises 13-16. 13. y' + x /y = 0, y(0) = 1 %3D b) dy 14. 3 = 2xy- y, y(2) = 1 dx dy 15. 4ху %3D dx y2 +4 (1) = 1 c) 33
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