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Use the method discussed under "Homogeneous Equa- tions" to solve Problems 9-16. 9. (xy + y²)dx – x² dy = 0 10. (3x² – y²)dx + (xy – x'y"!)dy = 0

Use the method discussed under "Homogeneous Equa- tions" to solve Problems 9-16. 9. (xy + y²)dx – x² dy = 0 10. (3x² – y²)dx + (xy – x'y"!)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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please solve question number 10,16,23 and 24
- y? y(In y – In x + 1) In Problems 1-8, identify (do not solve) the equation as homogeneous, Bernoulli, linear coefficients, or of the form y' = G(ax + by). 1. 2tx dx + (r? – xr²)dt = 0 2. (y – 4x – 1)? dx – dy = 0 3. dy/dx + y/x = x'y? 4. (t + x + 2)dx + (3t – x – 6)dt = 0 15. dx dy 16. dx 3xy Use the method discussed under "Equations of the Form dy/dx = G(ax + by) " to solve Problems 17-20. 17. dy/dx = Vx + y – 1 18. dy/dx = (x+y+2)² 19. dy/dx = (x – y + 5)² 20. dy/dx = sin(x – y) 5. 0 dy – y de = Vey de 6. (ye 2 + y³)dx - e e-2* dy = 0 Use the method discussed under "Bernoulli Equations" to solve Problems 21–28. -2x 7. cos(x + y)dy = sin(x + y)dx %3! 8. (y – by³)d® + 20²y dy = 0 dy y + 21. dx - x²y² dy 22. dx Use the method discussed under "Homogeneous Equa- - y = e*y tions" to solve Problems 9-16. 9. (xy + y²)dx – x² dy = 0 10. (3x² – y²)dx + (xy – x³y¯!)dy = 0 11. (y² – xy)dx + x² dy = 0 12. (x² + y²)dx + 2xy dy = 0 dy 2y 23. dx dy 24. dx y 5(x- 2)y/2 X - 2 13. dt dr_ x + rVF + dx 25. dt + tx' + = 0 26. dx + y = e'y2 %3D tx dy_0 sec(y/e) + y 14. de 2 + 2re dr 27. de dy 28. dx + y'x + y = 0
Transcribed Image Text:- y? y(In y – In x + 1) In Problems 1-8, identify (do not solve) the equation as homogeneous, Bernoulli, linear coefficients, or of the form y' = G(ax + by). 1. 2tx dx + (r? – xr²)dt = 0 2. (y – 4x – 1)? dx – dy = 0 3. dy/dx + y/x = x'y? 4. (t + x + 2)dx + (3t – x – 6)dt = 0 15. dx dy 16. dx 3xy Use the method discussed under "Equations of the Form dy/dx = G(ax + by) " to solve Problems 17-20. 17. dy/dx = Vx + y – 1 18. dy/dx = (x+y+2)² 19. dy/dx = (x – y + 5)² 20. dy/dx = sin(x – y) 5. 0 dy – y de = Vey de 6. (ye 2 + y³)dx - e e-2* dy = 0 Use the method discussed under "Bernoulli Equations" to solve Problems 21–28. -2x 7. cos(x + y)dy = sin(x + y)dx %3! 8. (y – by³)d® + 20²y dy = 0 dy y + 21. dx - x²y² dy 22. dx Use the method discussed under "Homogeneous Equa- - y = e*y tions" to solve Problems 9-16. 9. (xy + y²)dx – x² dy = 0 10. (3x² – y²)dx + (xy – x³y¯!)dy = 0 11. (y² – xy)dx + x² dy = 0 12. (x² + y²)dx + 2xy dy = 0 dy 2y 23. dx dy 24. dx y 5(x- 2)y/2 X - 2 13. dt dr_ x + rVF + dx 25. dt + tx' + = 0 26. dx + y = e'y2 %3D tx dy_0 sec(y/e) + y 14. de 2 + 2re dr 27. de dy 28. dx + y'x + y = 0
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