15. x(x + y)y' + y(3x + y) = 0 16. y = Vx+y+T 18. (x + y)y = 1 20. y'y +2xy = 6x 22. x'y +2xy = 5y 24. 2xy + y'e-2 = 2xy 25. y(xy + y)(1 +x*)2 =x 26. 3y?y' +y =e* 27. 3xy'y 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 Find general solutions of the differential equations in Prob- lems I through 30. Primes denote derivatives with respect to x throughout. 17. y = (4x + y)? 19. x'y' + 2xy = 5y 21. y' = y+y 23. xy' + 6y = 3xy/ 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. (x- y)y 2ry 12. xyy' = y +x4x² + y 13. xy = y+ Vx2 + y 14. yy +x = ? + y? 2. 2xyy' = x? + 2y² 4. (x - y)y =x + y %3! 8. x'y = xy +x'ea 10. xyy' = x + 3y? 1.6 Substitution Methods and Exact Equations 73 In Ruoblams l thuouglt 12 uarif aiuar diffauantial diff tiel