A.5.5: Section 5.5 Answers
( \newcommand{\kernel}{\mathrm{null}\,}\)
1. yp=cosx+2sinx
2. yp=cosx+(2−2x)sinx
3. yp=ex(−2cosx+3sinx)
4. yp=e2x2(cos2x−sin2x)
5. yp=−ex(xcosx−sinx)
6. yp=e−2x(1−2x)(cos3x−sin3x)
7. yp=x(cos2x−3sin2x)
8. yp=−x[(2−x)cosx+(3−2x)sinx]
9. yp=x[xcos(x2)−3sin(x2)]
10. yp=xe−x(3cosx+4sinx)
11. yp=xex[(−1+x)cos2x+(1+x)sin2x]
12. yp=−(14−10x)cosx−(2+8x−4x2)sinx
13. yp=(1+2x+x2)cosx+(1+3x2)sinx
14. yp=x22(cos2x−sin2x)
15. yp=ex(x2cosx+2sinx)
16. yp=ex(1−x2)(cosx+sinx)
17. yp=ex(x2−x3)(cosx+sinx)
18. yp=e−x[(1+2x)cosx−(1−3x)sinx]
19. yp=x(2cos3x−sin3x)
20. yp=−x3cosx+(x+2x2)sinx
21. yp=−e−x[(x+x2)cosx−(1+2x)sinx]
22. y=ex(2cosx+3sinx)+3ex−e6x
23. y=ex[(1+2x)cosx+(1−3x)sinx]
24. y=ex(cosx−2sinx)+e−3x(cosx+sinx)
25. y=e3x[(2+2x)cosx−(1+3x)sinx]
26. y=e3x[(2+3x)cosx+(4−x)sinx]+3ex−5e2x
27. yp=xe3x−ex5(cosx−2sinx)
28. yp=x(cosx+2sinx)−ex2(1−x)+e−x2
29. yp=−xex2(2+x)+2xe2x+110(3cosx+sinx)
30. yp=xex(cosx+xsinx)+ex25(4+5x)+1+x+x22
31. yp=x2e2x6(3+x)−e2x(cosx−sinx)+3e3x+14(2+x)
32. y=(1−2x+3x2)e2x+4cosx+3sinx
33. y=xe−2xcosx+3cos2x
34. y=−38cos2x+14sin2x+e−x−138e−2x−34xe−2x
40.
- 2xcosx−(2−x2)sinx+c
- −ex2[(1−x2)cosx−(1−x)2sinx]+c
- −e−x25[(4+10x)cos2x−(3−5x)sin2x]+c
- −e−x2[(1+x)2cosx−(1−x2)sinx]+c
- −ex2[x(3−3x+x2)cosx−(3−3x+x3)sinx]+c
- −ex[(1−2x)cosx+(1+x)sinx]+c
- e−x[xcosx+x(1+x)sinx]+c