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dy 3. (x – 3x²y) = xy² + y %3D - dx

dy 3. (x – 3x²y) = xy² + y %3D - dx

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 3 and 5
uation, v and hence is a function of y only, then a solution to the separa- is an integrating factor for the differential equation 1+Ce* y = v- = 1+0 EXERCISES 3.5 In each of Exercises 1–6, find integrating factors for the differential equation and then solve it. Use the result c tor and solve t 1. (x² + y²) dx – xy dy = 0 and 10. 2. (2y² – xy) dx + (xy – 2x²) dy = 0 9. (xy +x) d: 10. y dx + (2x dy 3. (x – 3x²y) = xy² + y dx In each of Exer equation has ho it. 4. (x² + y?)y' = 2xy 5. (2x2 + 3 y² – 2) dx – 2xy dy = 0 6. (3x + 2e) dx + xe dy = 0 11. (x² – y²) d. 12. (x² + y²) d- | 13. (y + xe"/x) y x cos 1. Show that multiplying the differential equation 14. (xc y + p(x)y = q(x) by el px) dx 15. Show that if converts the differential eguation into an exact one. 8. Show that if M has homoger Sx(x, y)-ry(x, y) r(x, y) I(x is an integran ble differential equation 16. Use the resul equation in E du S (x, y) -ry(x, y), dy r(x, y) Solve the differe 17. xy' + y = y
Transcribed Image Text:uation, v and hence is a function of y only, then a solution to the separa- is an integrating factor for the differential equation 1+Ce* y = v- = 1+0 EXERCISES 3.5 In each of Exercises 1–6, find integrating factors for the differential equation and then solve it. Use the result c tor and solve t 1. (x² + y²) dx – xy dy = 0 and 10. 2. (2y² – xy) dx + (xy – 2x²) dy = 0 9. (xy +x) d: 10. y dx + (2x dy 3. (x – 3x²y) = xy² + y dx In each of Exer equation has ho it. 4. (x² + y?)y' = 2xy 5. (2x2 + 3 y² – 2) dx – 2xy dy = 0 6. (3x + 2e) dx + xe dy = 0 11. (x² – y²) d. 12. (x² + y²) d- | 13. (y + xe"/x) y x cos 1. Show that multiplying the differential equation 14. (xc y + p(x)y = q(x) by el px) dx 15. Show that if converts the differential eguation into an exact one. 8. Show that if M has homoger Sx(x, y)-ry(x, y) r(x, y) I(x is an integran ble differential equation 16. Use the resul equation in E du S (x, y) -ry(x, y), dy r(x, y) Solve the differe 17. xy' + y = y
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