$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

1. $$y_{p}=2x^{3}$$

2. $$y_{p}=\frac{8}{105}x^{7/2}e^{-x^{2}}$$

3. $$y_{p}=x\ln |x|$$

4. $$y_{p}=-\frac{2(x^{2}+2)}{x}$$

5. $$y_{p}=-\frac{xe^{-3x}}{64}$$

6. $$y_{p}=-\frac{2x^{2}}{3}$$

7. $$y_{p}=-\frac{e^{-x}(x+1)}{x}$$

8. $$y_{p}=2x^{2}\ln |x|$$

9. $$y_{p}=x^{2}+1$$

10. $$y_{p}=\frac{2x^{2}+6}{3}$$

11. $$y_{p}=\frac{x^{2}\ln |x|}{3}$$

12. $$y_{p}=-x^{2}-2$$

13. $$\frac{1}{4}x^{3}\ln |x|-\frac{25}{48}x^{3}$$

14. $$y_{p}=\frac{x^{5/2}}{4}$$

15. $$y_{p}=\frac{x(12-x^{2})}{6}$$

16. $$y_{p}=\frac{x^{4}\ln |x|}{6}$$

17. $$y_{p}=\frac{x^{3}e^{x}}{2}$$

18. $$y_{p}=x^{2}\ln |x|$$

19. $$y_{p}=\frac{xe^{x}}{2}$$

20. $$y_{p}=\frac{3xe^{x}}{2}$$

21. $$y_{p}=-x^{3}$$

22. $$y=-x(\ln x)^{2}+3x+x^{3}-2x\ln x$$

23. $$y=\frac{x^{3}}{2}(\ln |x|)^{2}+x^{2}-x^{3}+2x^{3}\ln |x|$$

24. $$y=-\frac{1}{2}(3x+1)xe^{x}-3e^{x}-e^{2x}+4xe^{-x}$$

25. $$y=\frac{3}{2}x^{4}(\ln x)^{2}+3x-x^{4}+2x^{4}\ln x$$

26. $$y=-\frac{x^{4}+12}{6}+3x-x^{2}+2e^{x}$$

27. $$y=\left(\frac{x^{2}}{3}-\frac{x}{2}\right)\ln |x|+4x-2x^{2}$$

28. $$y=-\frac{xe^{x}(1+3x)}{2}+\frac{x+1}{2}-\frac{e^{x}}{4}+\frac{e^{3x}}{2}$$

29. $$y=-8x+2x^{2}-2x^{3}+2e^{x}-e^{-x}$$

30. $$y=3x^{2}\ln x-7x^{2}$$

31. $$y=\frac{3(4x^{2}+9)}{2}+\frac{x}{2}-\frac{e^{x}}{2}+\frac{e^{-x}}{2}+\frac{e^{2x}}{4}$$

32. $$y=x\ln x+x-\sqrt{x}+\frac{1}{x}+\frac{1}{\sqrt{x}}$$

33. $$y=x^{3}\ln |x|+x-2x^{3}+\frac{1}{x}-\frac{1}{x^{2}}$$

35. $$y_{p}=\int_{x_{0}}^{x}\frac{e^{(x-t)}-3e^{-(x-t)}+2e^{-2(x-t)} }{6}F(t)dt$$

36. $$y_{p}=\int_{x_{0}}^{x}\frac{(x-t)^{2}(2x+t)}{6xt^{3}}F(t)dt$$

37. $$y_{p}=\int_{x_{0}}^{x}\frac{xe^{(x-t)}-x^{2}+x(t-1) }{t^{4}}F(t)dt$$

38. $$y_{p}=\int_{x_{0}}^{x}\frac{x^{2}-t(t-2)-2te^{(x-t)}}{2x(t-1)^{2}}F(t)dt$$

39. $$y_{p}=\int_{x_{0}}^{x}\frac{e^{2(x-t)}-2e^{(x-t)}+2e^{-(x-t)}-e^{-2(x-t)}}{12}F(t)dt$$

40. $$y_{p}=\int_{x_{0}}^{x}\frac{(x-t)^{3}}{6x}F(t)dt$$

41. $$y_{p}=\int_{x_{0}}^{x}\frac{(x+t)(x-t)^{3}}{12x^{2}t^{3}}F(t)dt$$

42. $$y_{p}=\int_{x_{0}}^{x}\frac{e^{2(x-t)}(1+2x)+e^{-2(x-t)}(1-2t)-4x^{2}+4t^{2}-2}{32t^{2}}F(t)dt$$