Pregunta: 1.6 Problems 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 2. 2xyy' = x2 + 2y2 3. xy = y+2xy 4. (x - y)y' = x + y 5. x(x + y)y' = y(x - y) 6. (x + 2y)y' = y 7. xy2y = x + y3 8. x2y = xy + xey/x 9. x2y = xy+y? 10. xyy' = x2 + 3y2 11. (x2 - y2)y' =

1.6 Problems 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 2. 2xyy' = x2 + 2y2 3. xy = y+2xy 4. (x - y)y' = x + y 5. x(x + y)y' = y(x - y) 6. (x + 2y)y' = y 7. xy2y = x + y3 8. x2y = xy + xey/x 9. x2y = xy+y? 10. xyy' = x2 + 3y2 11. (x2 - y2)y' = 2xy 12. xyy' = y2 + x 4x2 + y2 13. xy' = y + x2 + y2 14. yy' + x = x2 + y2 15. x(x + y)y' + y(3x + y) = 0 16. y' = (x + y +1 17. y' = (4x + y)2 18. (x + y)y' = 1 19. x?y' + 2xy = 5y3 20. yy' + 2xy3 = 6x 21. y' = y + y3 22. xy' + 2xy = 5y4 23. xy' + 6y = 3x y 4/3 24. 2xy + y2e-2x = 2xy 25. y2(xy' + y)(1+x)1/2 = x 26. 3y2 y' + y = e-* 27. 3x y2 y' = 3x4 + y3 28. xe) y = 2(ey+x22x) 29. (2x sin y cos y)y' = 4x2 + siny 30. (x +eº y = x^2 - 1