A.9.4: Section 9.4 Answers

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