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# Section 5.7 Answers

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1. $$y_{p}=\frac{-\cos 3x\ln |\sec 3x+\tan 3x|}{9}$$

2. $$y_{p}=-\frac{\sin 2x\ln |\cos 2x|}{4}+\frac{x\cos 2x}{2}$$

3. $$y_{p} = 4e^{x} (1 + e^{x} ) \ln(1 + e^{−x} )$$

4. $$y_{p} = 3e^{x} (\cos x \ln | \cos x| + x \sin x)$$

5. $$y_{p}=\frac{8}{5}x^{7/2}e^{x}$$

6. $$y_{p}=e^{x}\ln (1-e^{-2x})-e^{-x}\ln (e^{2x}-1)$$

7. $$y_{p}=\frac{2(x^{3}-3)}{3}$$

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

9. $$y_{p}=x^{1/2}e^{x}\ln x$$

10. $$y_{p}=e^{-x(x+2)}$$

11. $$y_{p}=-4x^{5/2}$$

12. $$y_{p} = −2x^{2} \sin x−2x \cos x$$

13. $$y_{p}=-\frac{xe^{-x}(x+1)}{2}$$

14. $$y_{p}=-\frac{\sqrt{x}\cos\sqrt{x}}{2}$$

15. $$y_{p}=\frac{3x^{4}e^{x}}{2}$$

16. $$y_{p}=x^{a+1}$$

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

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

19. $$y_{p}=-e^{-x}\sin x$$

20. $$y_{p}=-\frac{\sqrt{x}}{2}$$

21. $$y_{p}=\frac{x^{3/2}}{4}$$

22. $$y_{p}=-3x^{2}$$

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

24. $$y_{p}=-\frac{4x^{3/2}}{15}$$

25. $$y_{p}=x^{3}e^{x}$$

26. $$y_{p}=xe^{x}$$

27. $$y_{p}=x^{2}$$

28. $$y_{p} = xe^{x} (x − 2)$$

29. $$y_{p}=\sqrt{x}e^{x}(x-1)/4$$

30. $$y=\frac{e^{2x}(3x^{2}-2x+6)}{6}+\frac{xe^{-x}}{3}$$

31. $$y = (x − 1)^{2} \ln(1 − x) + 2x^{2} − 5x + 3$$

32. $$y = (x^{2}−1)e^{x}−5(x−1)$$

33. $$y=\frac{x(x^{2}+6)}{3(x^{2}-1)}$$

34. $$y=-\frac{x^{2}}{2}+x+\frac{1}{2x^{2}}$$

35. $$y=\frac{x^{2}(4x+9)}{6(x+1)}$$

38.

1. $$y=k_{0}\cosh x+k_{1}\sinh x+\int _{0}^{x}\sinh (x-t)f(t)dt$$
2. $$y'=k_{0}\sinh x+k_{1}\cosh x+\int _{0}^{x}\cosh (x-t)f(t)dt$$

39.

1. $$y(x)=k_{0}\cos x+k_{1}\sin x+\int _{0}^{x}\sin (x-t)f(t)dt$$
2. $$y'(x)=-k_{0}\sin x+k_{1}\cos x+\int_{0}^{x}\cos (x-t)f(t)dt$$