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Mathematics LibreTexts

11.58: A.9.2- Section 9.2 Answers

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1. y=ex(c1+c2x+c3x2)

2. y=c1ex+c2ex+c3cos3x+c4sin3x

3. y=c1ex+c2cos4x+c3sin4x

4. y=c1ex+c2ex+c3e3x/2

5. y=c1ex+e2x(c1cosx+c2sinx)

6. y=c1ex+ex/2(c2+c3x)

7. y=ex/3(c1+c2x+c3x2)

8. y=c1+c2x+c3cosx+c4sinx

9. y=c1e2x+c2e2x+c3cos2x+c4sin2x

10. y=(c1+c2x)cos6x+(c3+c4x)sin6x

11. y=e3x/2(c1+c2x)+e3x/2(c3+c4x)

12. y=c1ex/2+c2ex/3+c3cosx+c4sinx

13. y=c1ex+c2e2x+c3ex/2+c4e3x/2

14. y=ex(c1+c2x+c3cosx+c4sinx)

15. y=cos2x2sin2x+e2x

16. y=2ex+3ex5e3x

17. y=2ex+3xex4ex

18. y=2excosx3exsinx+4e2x

19. y=95e5x/3+ex(1+2x)

20. y=e2x(13x+2x2)

21. y=e3x(2x)+4ex/2

22. y=ex/2(12x)+3ex/2

23. y=18(5e2x+e2x+10cos2x+4sin2x)

24. y=4ex+e2xe4x+2ex

25. y=2exex

26. y=e2x+e2x+ex(3cosx+sinx)

27. y=2ex/2+cos2xsin2x

28.

  1. {ex,xex,e2x}1
  2. {cos2x,sin2x,e3x}:26
  3. {excosx,exsinx,ex}:5
  4. {1,x,x2,ex}2ex
  5. {ex,ex,cosx,sinx}8
  6. {cosx,sinx,excosx,exsinx}:5

29. {e3xcos2x,e3xsin2x,e2x,xe2x,1,x,x2}

30. {ex,xex,ex/2,xex/2,x2ex/2,cosx,sinx}

31. {cos3x,xcos3x,x2cos3x,sin3x,xsin3x,x2sin3x,1,x}

32. {e2x,xe2x,x2e2x,ex,xex,1}

33. {cosx,sinx,cos3x,xcos3x,sin3x,xsin3x,e2x}

34. {e2x,xe2x,e2x,xe2x,cos2x,xcos2x,sin2x,xsin2x}

35. {ex/2cos2x,xex/2cos2x,x2ex/2cos2x,ex/2sin2x,xex/2sin2x,x2ex/2sin2x}

36. {1,x,x2,e2x,xe2x,cos2x,xcos2x,sin2x,xsin2x}

37. {cos(x/2),xcos(x/2),sin(x/2),xsin(x/2),cos2x/3xcos(2x/3),x2cos(2x/3),sin(2x/3),xsin(2x/3),x2sin(2x/3)}

38. {ex,e3x,excos2x,exsin2x}

39. b. e(a1+a2++an)x1i<jn(ajai)

43.

  1. {ex,ex/2cos(32x),ex/2sin(32x)}
  2. {ex,ex/2cos(32x),ex/2sin(32x)}
  3. {e2xcos2x,e2xsin2x,e2xcos2x,e2xsin2x}
  4. {ex,ex,ex/2cos(32x),ex/2sin(32x),ex/2cos(32x),ex/2sin(32x)}
  5. {cos2x,sin2x,e3xcosx,e3xsinx,e3xcosx,e3xsinx}
  6. {1,e2x,e3x/2cos(32x),e3x/2sin(32x),ex/2cos(32x),ex/2sin(32x)}
  7. {ex.ex/2cos(32x),ex/2sin(32x),ex/2cos(32x),ex/2sin(32x)}

45. y=c1xr1+c2xr2+c3xr3(r1,r2,r3 distinct);y=c1xr1+(c2+c3lnx)xr2(r1,r2 distinct);y=[c1+c2lnx+c3(lnx)2]xr1;y=c1xr1+xλ[c2cos(ωlnx)+c3sin(ωlnx)]


This page titled 11.58: A.9.2- Section 9.2 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

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