1. Linear: $y(x)=x^3(C+\ln x)$

2. Separable: $y(x)=x/(3-Cx-x\ln x)$

3. Homogeneous: $y(x)=x/(C-\ln x)$

4. Exact: $x^2{y}^3+e^x-\cos y=C$

5. Separable: $y(x)=C\exp (x^{-3}-x^{-2})$

6. Separable: $y(x)=x/(1+Cx+2x\ln x)$

7. Linear: $y(x)=x^{-2}(C+\ln x)$

8. Homogeneous: $y(x)=3Cx/(C-x^3)=3x/(1+K{x}^3)$

9. Bernoulli: $y(x)={(x^2+C{x}^{-1})}^2$

10. Separable: $y(x)=\tan (C+x+\frac{1}{3}{x}^3)$

11. Homogeneous: $y(x)=x/(C-3\ln x)$

12. Exact: $3x^2{y}^3+2{xy}^4=C$

13. Separable: $y(x)=1/(C+2x^2-x^5)$

14. Homogeneous: $y^2=x^2/(C+2\ln x)$

15. Linear: $y(x)=(x^3+C)e^{-3x}$

16. Substitution: $v=y-x$; solution: $y-x-1=C{e}^{2x}(y-x+1)$

17. Exact: $e^x+e^y+e^{xy}=C$

18. Homogeneous: $y^2={Cx}^2(x^2-y^2)$

19. Separable: $y(x)=x^2/(x^5+C{x}^2+1)$

20. Linear: $y(x)=2x^{-\mathrm{3/2}}+C{x}^{-3}$

21. Linear: $y(x)=[C+\ln (x-1)]/(x+1)$

22. Bernoulli: $y(x)={(2x^4+{Cx}^2)}^3$

23. Exact: ${xe}^y+y\sin x=C$

24. Separable: $y(x)=x^{\mathrm{1/2}}/(6x^2+C{x}^{\mathrm{1/2}}+2)$

25. Linear: $y\left(x\right)={\left(x+1\right)}^{-2}\left(x^3+3x^2+3x+C\right)=x+1+K{\left(x+1\right)}^{-2}$

26. Exact: $3x^{\mathrm{3/2}}{y}^{\mathrm{4/3}}-5x^{\mathrm{6/5}}{y}^{\mathrm{3/2}}=C$

27. Bernoulli: $y(x)=x^{-1}{(C+\ln x)}^{-\mathrm{1/3}}$

28. Linear: $y(x)=x^{-1}(C+e^{2x})$

29. Linear: $y(x)=(x^2+x+C){(2x+1)}^{-\mathrm{1/2}}$

30. Substitution: $v=x+y$; solution: $x=2{(x+y)}^{\mathrm{1/2}}-2\ln [1+{(x+y)}^{\mathrm{1/2}}]+C$

31. Separable and linear

32. Separable and Bernoulli

33. Exact and homogeneous

34. Exact and homogeneous

35. Separable and linear

36. Separable and Bernoulli