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Secțiunea 9.2 Răspunsuri

Secțiunea 9.2 Răspunsuri



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1. (y = e ^ {x} (c_ {1} + c_ {2} x + c_ {3} x ^ {2}) )

2. (y = c_ {1} e ^ {x} + c_ {2} e ^ {- x} + c_ {3} cos 3x + c_ {4} sin 3x )

3. (y = c_ {1} e ^ {x} + c_ {2} cos 4x + c_ {3} sin 4x )

4. (y = c_ {1} e ^ {x} + c_ {2} e ^ {- x} + c_ {3} e ^ {- 3x / 2} )

5. (y = c_ {1} e ^ {- x} + e ^ {- 2x} (c_ {1} cos x + c_ {2} sin x) )

6. (y = c_ {1} e ^ {x} + e ^ {x / 2} (c_ {2} + c_ {3} x) )

7. (y = e ^ {- x / 3} (c_ {1} + c_ {2} x + c_ {3} x ^ {2}) )

8. (y = c_ {1} + c_ {2} x + c_ {3} cos x + c_ {4} sin x )

9. (y = c_ {1} e ^ {2x} + c_ {2} e ^ {- 2x} + c_ {3} cos 2x + c_ {4} sin 2x )

10. (y = (c_ {1} + c_ {2} x) cos sqrt {6} x + (c_ {3} + c_ {4} x) sin sqrt {6} x )

11. (y = e ^ {3x / 2} (c_ {1} + c_ {2} x) + e ^ {- 3x / 2} (c_ {3} + c_ {4} x) )

12. (y = c_ {1} e ^ {- x / 2} + c_ {2} e ^ {- x / 3} + c_ {3} cos x + c_ {4} sin x )

13. (y = c_ {1} e ^ {x} + c_ {2} e ^ {- 2x} + c_ {3} e ^ {- x / 2} + c_ {4} e ^ {- 3x / 2} )

14. (y = e ^ {x} (c_ {1} + c_ {2} x + c_ {3} cos x + c_ {4} sin x) )

15. (y = cos 2x - 2 sin 2x + e ^ {2x} )

16. (y = 2e ^ {x} + 3e ^ {- x} - 5e ^ {- 3x} )

17. (y = 2e ^ {x} + 3xe ^ {x} - 4e ^ {- x} )

18. (y = 2e ^ {- x} cos x - 3e ^ {- x} sin x + 4e ^ {2x} )

19. (y = frac {9} {5} e ^ {- 5x / 3} + e ^ {x} (1 + 2x) )

20. (y = e ^ {2x} (1 - 3x + 2x ^ {2}) )

21. (y = e ^ {3x} (2 - x) + 4e ^ {- x / 2} )

22. (y = e ^ {x / 2} (1 - 2x) + 3e ^ {- x / 2} )

23. (y = frac {1} {8} (5e ^ {2x} + e ^ {- 2x} + 10 cos 2x + 4 sin 2x) )

24. (y = −4e ^ {x} + e ^ {2x} - e ^ {4x} + 2e ^ {- x} )

25. (y = 2e ^ {x} -e ^ {- x} )

26. (y = e ^ {2x} + e ^ {- 2x} + e ^ {- x} (3 cos x + sin x) )

27. (y = 2e ^ {- x / 2} + cos 2x - sin 2x )

28.

  1. ( {e ^ {x}, xe ^ {x}, e ^ {2x} } :: : 1 )
  2. ( { cos 2x, sin 2x, e ^ {3x} } :: : 26 )
  3. ( {e ^ {- x} cos x, e ^ {- x} sin x, e ^ {x} } :: : 5 )
  4. ( {1, x, x ^ {2}, e ^ {x} } : 2e ^ {x} )
  5. ( {e ^ {x}, e ^ {- x}, cos x, sin x } : 8 )
  6. ( { cos x, sin x, e ^ {x} cos x, e ^ {x} sin x } :: : 5 )

29. ( {e ^ {- 3x} cos 2x, e ^ {- 3x} sin 2x, e ^ {2x}, xe ^ {2x}, 1, x, x ^ {2} } )

30. ( {e ^ {x}, xe ^ {x}, e ^ {x / 2}, xe ^ {x / 2}, x ^ {2} e ^ {x / 2}, cos x , sin x } )

31. ( { cos 3x, x cos 3x, x ^ {2} cos 3x, sin 3x, x sin 3x, x ^ {2} sin 3x, 1, x } )

32. ( {e ^ {2x}, xe ^ {2x}, x ^ {2} e ^ {2x}, e ^ {- x}, xe ^ {- x}, 1 } )

33. ( { cos x, sin x, cos 3x, x cos 3x, sin 3x, x sin 3x, e ^ {2x} } )

34. ( {e ^ {2x}, xe ^ {2x}, e ^ {- 2x}, xe ^ {- 2x}, cos 2x, x cos 2x, sin 2x, x sin 2x } )

35. ( {e ^ {- x / 2} cos 2x, xe ^ {- x / 2} cos 2x, x ^ {2} e ^ {- x / 2} cos 2x, e ^ { −x / 2} sin 2x, xe ^ {- x / 2} sin 2x, x ^ {2} e ^ {- x / 2} sin 2x } )

36. ( {1, x, x ^ {2}, e ^ {2x}, xe ^ {2x}, cos 2x, x cos 2x, sin 2x, x sin 2x } )

37. ( { cos (x / 2), x cos (x / 2), sin (x / 2), x sin (x / 2), cos 2x / 3 x cos (2x / 3), x ^ {2} cos (2x / 3), sin (2x / 3), x sin (2x / 3), x ^ {2} sin (2x / 3) } )

38. ( {e ^ {- x}, e ^ {3x}, e ^ {x} cos 2x, e ^ {x} sin 2x } )

39. b. (e ^ {(a_ {1} + a_ {2} + ldots + a_ {n}) x} prod_ {1 leq i

43.

  1. ( {e ^ {x}, e ^ {- x / 2} cos left ( frac { sqrt {3}} {2} x right), e ^ {- x / 2} sin left ( frac { sqrt {3}} {2} x right) } )
  2. ( {e ^ {- x}, e ^ {x / 2} cos left ( frac { sqrt {3}} {2} x right), e ^ {x / 2} sin stânga ( frac { sqrt {3}} {2} x dreapta) } )
  3. ( {e ^ {2x} cos 2x, e ^ {2x} sin 2x, e ^ {- 2x} cos 2x, e ^ {- 2x} sin 2x } )
  4. ( {e ^ {x}, e ^ {- x}, e ^ {x / 2} cos left ( frac { sqrt {3}} {2} x right), e ^ {x / 2} sin left ( frac { sqrt {3}} {2} x right), e ^ {- x / 2} cos left ( frac { sqrt {3}} {2} x right), e ^ {- x / 2} sin left ( frac { sqrt {3}} {2} x right) } )
  5. ( { cos 2x, sin 2x, e ^ {- sqrt {3x}} cos x, e ^ {- sqrt {3x}} sin x, e ^ { sqrt {3x}} cos x, e ^ { sqrt {3x}} sin x } )
  6. ( {1, e ^ {2x}, e ^ {3x / 2} cos left ( frac { sqrt {3}} {2} x right), e ^ {3x / 2} sin left ( frac { sqrt {3}} {2} x right), e ^ {x / 2} cos left ( frac { sqrt {3}} {2} x right), e ^ {x / 2} sin left ( frac { sqrt {3}} {2} x right) } )
  7. ( {e ^ {- x}. e ^ {x / 2} cos left ( frac { sqrt {3}} {2} x right), e ^ {x / 2} sin left ( frac { sqrt {3}} {2} x right), e ^ {- x / 2} cos left ( frac { sqrt {3}} {2} x right), e ^ {- x / 2} sin left ( frac { sqrt {3}} {2} x right) } )

45. (y = c_ {1} x ^ {r_ {1}} + c_ {2} x ^ {r_ {2}} + c_ {3} x ^ {r_ {3}} : (r_ {1 }, r_ {2}, r_ {3} text {distinct)}; : y = c_ {1} x ^ {r_ {1}} + (c_ {2} + c_ {3} ln x) x ^ {r_ {2}} : (r_ {1}, r_ {2} text {distinct)}; : y = [c_ {1} + c_ {2} ln x + c_ {3} ( ln x) ^ {2}] x ^ {r_ {1}}; : y = c_ {1} x ^ {r_ {1}} + x ^ { lambda} [c_ {2} cos ( omega ln x) + c_ {3} sin ( omega ln x)] )


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