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9. e* (y² – 4y) dx +4 dy = 0 |

9. e* (y² – 4y) dx +4 dy = 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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Number 9 show all work from 3.2
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 d: 17. a) Solve the equar dy 3. dx for y. b) Use the result = x? + 2xy 4. sin xy' = xy + 4x of x for which Solve the differential equations in Exercises 5–12. 5. y' = 2x?y – 4y problem in Exe 18. a) Solve the equat 6. e* y dx+4y³ dy = 0 for y. b) Use the result of 7. (x² + 1) = xy? + x dx dy 8. sec xy' – xy/(y+4) = 0 9. e (y² – 4y) dx +4 dy = 0 x²y° +3xy³ 2x?y of x for which t problem in Exern dy 10. dx dy, dy 11. t 19. Use Maple (or ano age) to graph the soli = te dt dt dr =r sin 0 do 20. Use Maple (or anot age) to graph the solum 12. (r2 + 1) cos 0 21. a) Show that the equamu separable. Solve the initial value problems in Exercises 13-16. 13. y' +x²/y = 0, y(0) = 1 dy b) Show that the subst converts the differem 14.3 = 2xy – y, y(2) = 1 dx %3D a separable one. dy 4ху c) Solve the different 15. dx y2 +4' Y(1) = 1 3.3 EXACT DIFFERENTIAL EQUATIONS F(x, y)=C
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 d: 17. a) Solve the equar dy 3. dx for y. b) Use the result = x? + 2xy 4. sin xy' = xy + 4x of x for which Solve the differential equations in Exercises 5–12. 5. y' = 2x?y – 4y problem in Exe 18. a) Solve the equat 6. e* y dx+4y³ dy = 0 for y. b) Use the result of 7. (x² + 1) = xy? + x dx dy 8. sec xy' – xy/(y+4) = 0 9. e (y² – 4y) dx +4 dy = 0 x²y° +3xy³ 2x?y of x for which t problem in Exern dy 10. dx dy, dy 11. t 19. Use Maple (or ano age) to graph the soli = te dt dt dr =r sin 0 do 20. Use Maple (or anot age) to graph the solum 12. (r2 + 1) cos 0 21. a) Show that the equamu separable. Solve the initial value problems in Exercises 13-16. 13. y' +x²/y = 0, y(0) = 1 dy b) Show that the subst converts the differem 14.3 = 2xy – y, y(2) = 1 dx %3D a separable one. dy 4ху c) Solve the different 15. dx y2 +4' Y(1) = 1 3.3 EXACT DIFFERENTIAL EQUATIONS F(x, y)=C
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