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Solve the differential equa 5. y' = 2x?y – 4y %3D

Solve the differential equa 5. y' = 2x?y – 4y %3D

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 Equations 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 16. ye dy - sec y dx 17. a) Solve the equat for y. b) Use the result dy 3. dx = x² + 2xy 4. sin xy' = xy +4x of x for which problem in Ex 18. a) Solve the equ. Solve the differential equations in Exercises 5-12. 5. y' = 2x?y – 4y dy 6. e* y dx+4y³ dy = 0 for y. 7. (x² + 1) = xy² + x dx b) Use the resul of x for whic 8. sec xy' - xy/(y+4) = 0 9. e* (y? – 4y) dx +4 dy = 0 dy x?y3 + 3xy³ 2x?y problem in E dy 11. t dt dy = te dt 19. Use Maple (or age) to graph th 10. dx dr =r sin 0 de 20. Use Maple (oD age) to graph t 12. (r2 + 1) cos 0 Solve the initial value problems in Exercises 13-16. 13. y' + x²/y = 0, y(0) = 1 21. a) Show that separable. b) Show that dy 14. 3 = 2xy – y, y(2) = 1 dx converts t %3D a separab dy 15. 4xy y(1) = 1 y2 +4' c) Solve the |3| dx 3.3 EXACT DIFFERENTIAL EQUATIONS In the last section we learned how to solve separabl the equa
Transcribed Image Text:First Order Ordinary Differential Equations 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 16. ye dy - sec y dx 17. a) Solve the equat for y. b) Use the result dy 3. dx = x² + 2xy 4. sin xy' = xy +4x of x for which problem in Ex 18. a) Solve the equ. Solve the differential equations in Exercises 5-12. 5. y' = 2x?y – 4y dy 6. e* y dx+4y³ dy = 0 for y. 7. (x² + 1) = xy² + x dx b) Use the resul of x for whic 8. sec xy' - xy/(y+4) = 0 9. e* (y? – 4y) dx +4 dy = 0 dy x?y3 + 3xy³ 2x?y problem in E dy 11. t dt dy = te dt 19. Use Maple (or age) to graph th 10. dx dr =r sin 0 de 20. Use Maple (oD age) to graph t 12. (r2 + 1) cos 0 Solve the initial value problems in Exercises 13-16. 13. y' + x²/y = 0, y(0) = 1 21. a) Show that separable. b) Show that dy 14. 3 = 2xy – y, y(2) = 1 dx converts t %3D a separab dy 15. 4xy y(1) = 1 y2 +4' c) Solve the |3| dx 3.3 EXACT DIFFERENTIAL EQUATIONS In the last section we learned how to solve separabl the equa
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