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18. (x + y)y' = 1 20. yy +2xy = 6x 22. x'y' +2xy 5y* 24. 2xy' + y'e 25. y?(xy + y)(1 +x*)/2 =x 26. 3y'y + y =e"* 19. 21. 23. -2 = 2xy

18. (x + y)y' = 1 20. yy +2xy = 6x 22. x'y' +2xy 5y* 24. 2xy' + y'e 25. y?(xy + y)(1 +x*)/2 =x 26. 3y'y + y =e"* 19. 21. 23. -2 = 2xy

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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please send handwritten solution for Q 22 1.6
1.6 Problems Find general solutions of the differential equations in Prob- lems i through 30. Primes denote derivatives with respect to x throughout. 15. x(x + y)y' + y(3x + y) = 0 16. y = Vx + y +1 18. (x + y)y = 1 20. y?y' + 2xy = 6x 22. x'y + 2xy = 5y* 24. 2xy' + y'e-24 = 2xy 25. y?(xy' + y)(1 +x*)/2 = x 26. 3y?y' + y' = e* 27. 3xyy = 3x* + y 28. xe' y = 2(e +x'e) 29. (2x sin y cos y)y' 4x +sin' y 30. (x +e)y' = xe – 1 17. y = (4x + y)? 19. xy' + 2ry 5y 21. y' = y + y 23. xy' + 6y = 3xyt/3 1. (x + y)y = x - y 3. xy = y +2xy 5. x(x+ y)y' = y(x – y) 6. (x + 2y)y' y 7. xy'y' = x + y 9. x'y = xy + y 11. (x² – y?)y = 2ry 12. xyy' = y? + x/4x? + y? 13. xy = y +Vr + y? 14. yy +x = x² + y? 2. 2xyy' = x? + 2y? 4. (x - y)y' = x+ y %3D 8. x'y' = xy + x'erla 10. xyy' = x? +3y? 1.6 Substitution Methods and Exact Equations 73 In Problems 31 through 42, verify that the given differential equation is exact; then solve it. 60. Use the method in Problem 59 to solve the differential equation dy 2y-x +7 31. (2x + 3y) dx + (3x +2y) dy = 0 32. (4x - y) dx + (6y – x) dy = 0 33. (3x? +2y?) dx+ (4xy +6y?) dy = 0 34. (2xy + 3x?) dx + (2x'y+4y) dy = 0 35. (x' +2) dx + (y² + In x) dy = 0 dx 4x – 3y – 18 61. Make an appropriate substitution to find a solution of the equation dy/dx = sin(x – y). Does this general solution contain the linear solution y(x) = x - 1/2 that is readily verified by substitution in the differential equation? 62. Show that the solution curves of the differential equation 36. (1 + ye") dx + (2y + xe) dy = 0 y(2r - y) x(2y3 - x) 37. (cos x + In y) dx + dy = 0 dy dx
Transcribed Image Text:1.6 Problems Find general solutions of the differential equations in Prob- lems i through 30. Primes denote derivatives with respect to x throughout. 15. x(x + y)y' + y(3x + y) = 0 16. y = Vx + y +1 18. (x + y)y = 1 20. y?y' + 2xy = 6x 22. x'y + 2xy = 5y* 24. 2xy' + y'e-24 = 2xy 25. y?(xy' + y)(1 +x*)/2 = x 26. 3y?y' + y' = e* 27. 3xyy = 3x* + y 28. xe' y = 2(e +x'e) 29. (2x sin y cos y)y' 4x +sin' y 30. (x +e)y' = xe – 1 17. y = (4x + y)? 19. xy' + 2ry 5y 21. y' = y + y 23. xy' + 6y = 3xyt/3 1. (x + y)y = x - y 3. xy = y +2xy 5. x(x+ y)y' = y(x – y) 6. (x + 2y)y' y 7. xy'y' = x + y 9. x'y = xy + y 11. (x² – y?)y = 2ry 12. xyy' = y? + x/4x? + y? 13. xy = y +Vr + y? 14. yy +x = x² + y? 2. 2xyy' = x? + 2y? 4. (x - y)y' = x+ y %3D 8. x'y' = xy + x'erla 10. xyy' = x? +3y? 1.6 Substitution Methods and Exact Equations 73 In Problems 31 through 42, verify that the given differential equation is exact; then solve it. 60. Use the method in Problem 59 to solve the differential equation dy 2y-x +7 31. (2x + 3y) dx + (3x +2y) dy = 0 32. (4x - y) dx + (6y – x) dy = 0 33. (3x? +2y?) dx+ (4xy +6y?) dy = 0 34. (2xy + 3x?) dx + (2x'y+4y) dy = 0 35. (x' +2) dx + (y² + In x) dy = 0 dx 4x – 3y – 18 61. Make an appropriate substitution to find a solution of the equation dy/dx = sin(x – y). Does this general solution contain the linear solution y(x) = x - 1/2 that is readily verified by substitution in the differential equation? 62. Show that the solution curves of the differential equation 36. (1 + ye") dx + (2y + xe) dy = 0 y(2r - y) x(2y3 - x) 37. (cos x + In y) dx + dy = 0 dy dx
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