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Find general solutions of the differential equations in Prob- lems 1 through 30. Primes denote derivatives with respect to x throughout. 2. 2xyy' = x² + 2y² 4. (x – y)y' = x + y 6. (x + 2y)y' = y 8. x²y' = xy +x²ev/x 10. xyy' = x2 + 3y2 1. (x + y)y' = x – y 3. xy' = y + 2/xy 5. x(x + y)y' 7. xy2y' = x³ + y³ 9. х2у 3 ху + у? 11. (x² – y²)y' = 2xy 12. xyy' = y2 + x /4x² + y2 13. xy' = y + Vx² + y2 14. yy' +x = Vx2 + y2 15. x(x + y)y' + y(3x + y) = 0 16. y' = /x + y +I 18. (x + y)y' = 1 20. y²y' + 2xy³ = 6x 22. x2y' + 2xy = 5y4 24. 2xy' + y³e-2x = 2xy 25. y2(xy' + y)(1+x4)\/2 = x 26. 3y²y' + y³ = e¯* 27. 3xv2 v' = 3x4 + v3 у (х — у) 2xy | 17. y' = (4x + y)² 19. x²y' + 2xy = 5y3 21. у'3D у + у3 23. ху' + бу — 3ху4/3

Find general solutions of the differential equations in Prob- lems 1 through 30. Primes denote derivatives with respect to x throughout. 2. 2xyy' = x² + 2y² 4. (x – y)y' = x + y 6. (x + 2y)y' = y 8. x²y' = xy +x²ev/x 10. xyy' = x2 + 3y2 1. (x + y)y' = x – y 3. xy' = y + 2/xy 5. x(x + y)y' 7. xy2y' = x³ + y³ 9. х2у 3 ху + у? 11. (x² – y²)y' = 2xy 12. xyy' = y2 + x /4x² + y2 13. xy' = y + Vx² + y2 14. yy' +x = Vx2 + y2 15. x(x + y)y' + y(3x + y) = 0 16. y' = /x + y +I 18. (x + y)y' = 1 20. y²y' + 2xy³ = 6x 22. x2y' + 2xy = 5y4 24. 2xy' + y³e-2x = 2xy 25. y2(xy' + y)(1+x4)\/2 = x 26. 3y²y' + y³ = e¯* 27. 3xv2 v' = 3x4 + v3 у (х — у) 2xy | 17. y' = (4x + y)² 19. x²y' + 2xy = 5y3 21. у'3D у + у3 23. ху' + бу — 3ху4/3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find general solutions of the differential equations in Prob- lems 1 through 30. Primes denote derivatives with respect to x throughout. 1. (x + y)y' = x – y 3. xy' = y + 2/xy 5. x(x + y)y' 7. xy²y' = x³ + y³ 9. x²y' = xy + y² 11. (x² – y²)y' = 2xy 12. xyy' = y2 + x /4x² + y2 13. xy' = y + Vx2 + y2 14. yy' +x = Vx² + y² 15. x(x + y)y' + y(3x + y) = 0 16. y' = x + y +I 18. (x + y)y' = 1 20. y²y' + 2xy³ = 6x 22. x2y' + 2xy = 5y4 24. 2xy' + y³e-2x = 2xy 25. y2(xy' + y)(1+x4)\/2 = x 26. 3y2 y' + y3 = e¬x 27. 3xy?y' = 3x4 + y3 28. xe' y' = 2(e + x³e2x) 29. (2x sin y cos y)y' = 4x² + sin? y 30. (x + e')y' = xe¯y – 1 2. 2xyy' = x² + 2y² 4. (x – y)y' = x + y 6. (x + 2y)y' = y 8. x²y' = xy +x²ev/x 10. xyy' = x2 + 3y² у (х — у) | 17. y' = (4x + y)² 19. x²y' + 2xy = 5y³ 21. y' = y + y3 23. ху' + бу — 3ху4/3
Transcribed Image Text:Find general solutions of the differential equations in Prob- lems 1 through 30. Primes denote derivatives with respect to x throughout. 1. (x + y)y' = x – y 3. xy' = y + 2/xy 5. x(x + y)y' 7. xy²y' = x³ + y³ 9. x²y' = xy + y² 11. (x² – y²)y' = 2xy 12. xyy' = y2 + x /4x² + y2 13. xy' = y + Vx2 + y2 14. yy' +x = Vx² + y² 15. x(x + y)y' + y(3x + y) = 0 16. y' = x + y +I 18. (x + y)y' = 1 20. y²y' + 2xy³ = 6x 22. x2y' + 2xy = 5y4 24. 2xy' + y³e-2x = 2xy 25. y2(xy' + y)(1+x4)\/2 = x 26. 3y2 y' + y3 = e¬x 27. 3xy?y' = 3x4 + y3 28. xe' y' = 2(e + x³e2x) 29. (2x sin y cos y)y' = 4x² + sin? y 30. (x + e')y' = xe¯y – 1 2. 2xyy' = x² + 2y² 4. (x – y)y' = x + y 6. (x + 2y)y' = y 8. x²y' = xy +x²ev/x 10. xyy' = x2 + 3y² у (х — у) | 17. y' = (4x + y)² 19. x²y' + 2xy = 5y³ 21. y' = y + y3 23. ху' + бу — 3ху4/3
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