1. Linear: y(x)=x3(C+ln x)
2. Separable: y(x)=x/(3−Cx−xln x)
3. Homogeneous: y(x)=x/(C−ln x)
4. Exact: x2y3+ex−cos y=C
5. Separable: y(x)=Cexp(x−3−x−2)
6. Separable: y(x)=x/(1+Cx+2xln x)
7. Linear: y(x)=x−2(C+ln x)
8. Homogeneous: y(x)=3Cx/(C−x3)=3x/(1+Kx3)
9. Bernoulli: y(x)=(x2+Cx−1)2
10. Separable: y(x)=tan(C+x+13x3)
11. Homogeneous: y(x)=x/(C−3 ln x)
12. Exact: 3x2y3+2xy4=C
13. Separable: y(x)=1/(C+2x2−x5)
14. Homogeneous: y2=x2/(C+2 ln x)
15. Linear: y(x)=(x3+C)e−3x
16. Substitution: v=y−x; solution: y−x−1=Ce2x(y−x+1)
17. Exact: ex+ey+exy=C
18. Homogeneous: y2=Cx2(x2−y2)
19. Separable: y(x)=x2/(x5+Cx2+1)
20. Linear: y(x)=2x−3/2+Cx−3
21. Linear: y(x)=[C+ln(x−1)]/(x+1)
22. Bernoulli: y(x)=(2x4+Cx2)3
23. Exact: xey+y sin x=C
24. Separable: y(x)=x1/2/(6x2+Cx1/2+2)
25. Linear: y(x)=(x+1)−2(x3+3x2+3x+C)=x+1+K(x+1)−2
26. Exact: 3x3/2y4/3−5x6/5y3/2=C
27. Bernoulli: y(x)=x−1(C+ln x)−1/3
28. Linear: y(x)=x−1(C+e2x)
29. Linear: y(x)=(x2+x+C)(2x+1)−1/2
30. Substitution: v=x+y; solution: x=2(x+y)1/2−2 ln[1+(x+y)1/2]+C
31. Separable and linear
32. Separable and Bernoulli
33. Exact and homogeneous
34. Exact and homogeneous
35. Separable and linear
36. Separable and Bernoulli