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1. $$y_{p}=\cos x+2\sin x$$

2. $$y_{p}=\cos x+(2-2x)\sin x$$

3. $$y_{p}=e^{x}(-2\cos x+3\sin x)$$

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

5. $$y_{p}=-e^{x}(x\cos x-\sin x)$$

6. $$y_{p} = e^{−2x} (1 − 2x)(\cos 3x − \sin 3x)$$

7. $$y_{p} = x(\cos 2x − 3 \sin 2x)$$

8. $$y_{p} = −x [(2 − x) \cos x + (3 − 2x) \sin x]$$

9. $$y_{p}=x\left[x\cos\left(\frac{x}{2}\right)-3\sin\left(\frac{x}{2}\right) \right]$$

10. $$y_{p} = xe^{−x} (3 \cos x + 4 \sin x)$$

11. $$y_{p} = xe^{x} [(−1 + x) \cos 2x + (1 + x) \sin 2x]$$

12. $$y_{p} = −(14 − 10x) \cos x − (2 + 8x − 4x^{2} ) \sin x$$

13. $$y_{p} = (1 + 2x + x^{2}) \cos x + (1 + 3x^{2}) \sin x$$

14. $$y_{p}=\frac{x^{2}}{2}(\cos 2x-\sin 2x)$$

15. $$y_{p} = e^{x} (x^{2} \cos x + 2 \sin x)$$

16. $$y_{p} = e^{x} (1 − x^{2} )(\cos x + \sin x)$$

17. $$y_{p} = e^{x} (x^{2} − x^{3})(\cos x + \sin x)$$

18. $$y_{p} = e^{−x} [(1 + 2x) \cos x − (1 − 3x) \sin x]$$

19. $$y_{p} = x(2 \cos 3x − \sin 3x)$$

20. $$y_{p} = −x^{3} \cos x + (x + 2x^{2} ) \sin x$$

21. $$y_{p} = −e^{−x}[ (x + x^{2} ) \cos x − (1 + 2x) \sin x]$$

22. $$y = e^{x} (2 \cos x + 3 \sin x) + 3e^{x} − e^{6x}$$

23. $$y = e^{x} [(1 + 2x) \cos x + (1 − 3x) \sin x]$$

24. $$y = e^{x} (\cos x−2 \sin x)+e^{−3x} (\cos x+\sin x)$$

25. $$y = e^{3x} [(2 + 2x) \cos x − (1 + 3x) \sin x]$$

26. $$y = e^{3x} [(2 + 3x) \cos x + (4 − x) \sin x]+3e^{x}−5e^{2x}$$

27. $$y_{p}=xe^{3x}-\frac{e^{x}}{5}(\cos x-2\sin x)$$

28. $$y_{p}=x(\cos x +2\sin x)-\frac{e^{x}}{2}(1-x)+\frac{e^{-x}}{2}$$

29. $$y_{p}=-\frac{xe^{x}}{2}(2+x)+2xe^{2x}+\frac{1}{10}(3\cos x+\sin x)$$

30. $$y_{p}=xe^{x}(\cos x+x\sin x)+\frac{e^{x}}{25}(4+5x)+1+x+\frac{x^{2}}{2}$$

31. $$y_{p}=\frac{x^{2}e^{2x}}{6}(3+x)-e^{2x}(\cos x-\sin x)+3e^{3x}+\frac{1}{4}(2+x)$$

32. $$y = (1 − 2x + 3x^{2})e^{2x} + 4 \cos x + 3 \sin x$$

33. $$y = xe^{−2x} \cos x + 3 \cos 2x$$

34. $$y=-\frac{3}{8}\cos 2x+\frac{1}{4}\sin 2x+e^{-x}-\frac{13}{8}e^{-2x}-\frac{3}{4}xe^{-2x}$$

40.

1. $$2x \cos x − (2 − x^{2}) \sin x + c$$
2. $$-\frac{e^{x}}{2}\left[ (1-x^{2})\cos x-(1-x)^{2}\sin x\right] +c$$
3. $$-\frac{e^{-x}}{25}[(4+10x)\cos 2x-(3-5x)\sin 2x]+c$$
4. $$-\frac{e^{-x}}{2}\left[ (1+x)^{2}\cos x-(1-x^{2})\sin x\right]+c$$
5. $$-\frac{e^{x}}{2}\left[x(3-3x+x^{2})\cos x-(3-3x+x^{3})\sin x \right]+c$$
6. $$-e^{x}[(1-2x)\cos x+(1+x)\sin x]+c$$
7. $$e^{-x}[x\cos x+x(1+x)\sin x]+c$$