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EXERCISES 2.5 Each DE in Problems 1-14 is homogeneous. Each DE in In Problems 1-10 solve the given differential equation by using an appropriate substitution. In Problem using an ap 1. (x-y) dx +x dy 3. x dr + (y - 20) dy - 0 4. y dx = 2(x+ y) dy 5. (y + yx) dr – x*dy = 0 0 2 (x+ y) dx + xdy = 0 23. 25. dx

EXERCISES 2.5 Each DE in Problems 1-14 is homogeneous. Each DE in In Problems 1-10 solve the given differential equation by using an appropriate substitution. In Problem using an ap 1. (x-y) dx +x dy 3. x dr + (y - 20) dy - 0 4. y dx = 2(x+ y) dy 5. (y + yx) dr – x*dy = 0 0 2 (x+ y) dx + xdy = 0 23. 25. dx

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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EXERCISES 2.5 Each DE in Problems 23-30 is of the form given in (5). In Problems 23-28 solve the given differential equation by using an appropriate substitution. Each DE in Problems 1-14 is homogeneous. In Problems 1-10 solve the given differential cquation by using an appropriate substitution. 1. (x- y) dx + x dy -0 2. (x + y) dx +xdy 0 3. x dx + (y - 21) dy =0 4. y dr = 2(x + y) dy 23. dx = (x + y + 1 24. dx 5. (y + yx) dx - dy = 0 25. = tan'(x + y) 26. dx sin(x dx 6. (y + yx) dx + x dy 0 dy 27. dx - 2+ Vy - 2r +3 28. 7. xp dx y+x In Problems 29 and 30 solve the given initial-value problem. dy x + 3y 8. dx 3x + y dy 29. - cos(x + y). y(0) = m/4 dx 9. -y dx + (x + Vay) dy = 0 dy 30. 3r+2y dz 3r + 2y + 2 y(-1) = -1 10. - y + V- y. x>0 dx In Problems 11-14 solve the given initial-value problem. 11. xy - y - . y(1) = 2 12. ( + xy. yt-1) = 1 13. (x+ ye) dx – xe dy = 0, y(1) = 0 14. yde + x(ln x - In y- 1) dy 0, y(1) =e Each DE in Problems 1s-22is a Bernoulli equation. In Problems 15-20 solve the given differential equation by using an appropriate substitution. 16. 17. dx = y(xy' - 1) 18. x dx :-(1 + xày = ay 19. +y = ty 20. 3(1 + 2ry(y-1) In Problems 21 and 22 solve the given initial-value problem. 21. - 2xy 3y'. y) - 22. ya + y - 1. y(0) = 4 dx
Transcribed Image Text:EXERCISES 2.5 Each DE in Problems 23-30 is of the form given in (5). In Problems 23-28 solve the given differential equation by using an appropriate substitution. Each DE in Problems 1-14 is homogeneous. In Problems 1-10 solve the given differential cquation by using an appropriate substitution. 1. (x- y) dx + x dy -0 2. (x + y) dx +xdy 0 3. x dx + (y - 21) dy =0 4. y dr = 2(x + y) dy 23. dx = (x + y + 1 24. dx 5. (y + yx) dx - dy = 0 25. = tan'(x + y) 26. dx sin(x dx 6. (y + yx) dx + x dy 0 dy 27. dx - 2+ Vy - 2r +3 28. 7. xp dx y+x In Problems 29 and 30 solve the given initial-value problem. dy x + 3y 8. dx 3x + y dy 29. - cos(x + y). y(0) = m/4 dx 9. -y dx + (x + Vay) dy = 0 dy 30. 3r+2y dz 3r + 2y + 2 y(-1) = -1 10. - y + V- y. x>0 dx In Problems 11-14 solve the given initial-value problem. 11. xy - y - . y(1) = 2 12. ( + xy. yt-1) = 1 13. (x+ ye) dx – xe dy = 0, y(1) = 0 14. yde + x(ln x - In y- 1) dy 0, y(1) =e Each DE in Problems 1s-22is a Bernoulli equation. In Problems 15-20 solve the given differential equation by using an appropriate substitution. 16. 17. dx = y(xy' - 1) 18. x dx :-(1 + xày = ay 19. +y = ty 20. 3(1 + 2ry(y-1) In Problems 21 and 22 solve the given initial-value problem. 21. - 2xy 3y'. y) - 22. ya + y - 1. y(0) = 4 dx
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