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Asylum15

Differentiation Question! :(

  • one year ago
  • one year ago

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  1. Asylum15
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    If y = \[5e ^{-4t} - 3e ^{-2t}\] show that \[\frac{ d^2y }{ dt^2 } + 6\frac{ dy }{ dt } +8y = 0\]

    • one year ago
  2. Asylum15
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    Derive Y?

    • one year ago
  3. mark_o.
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    use the formula D(e^u)= e^u D(u) lets see what will you get

    • one year ago
  4. Asylum15
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    So Y' = -4(5e^-4t) + 2 (-3e^-2t) ?

    • one year ago
  5. Asylum15
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    e^ax = ae^ax

    • one year ago
  6. mark_o.
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    De^ax = ae^ax yup

    • one year ago
  7. Asylum15
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    So my first step is correct?

    • one year ago
  8. mark_o.
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    ah +3

    • one year ago
  9. Asylum15
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    \[= -4(5e ^{-4t}) + 2(-3e ^{-2t})\]

    • one year ago
  10. Asylum15
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    ?

    • one year ago
  11. mark_o.
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    sorry about that i dint solved it my self but im just guiding you to the right solution :D

    • one year ago
  12. Asylum15
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    So am i right so far?

    • one year ago
  13. mark_o.
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    yes correct :D

    • one year ago
  14. Asylum15
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    Ok, what should I do next? :)

    • one year ago
  15. mark_o.
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    now do the 2nd derivative

    • one year ago
  16. Asylum15
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    Y'' yeah?

    • one year ago
  17. mark_o.
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    yup but you can still simplify that one by multiplying the constant coefficients

    • one year ago
  18. Asylum15
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    -4 multipled by 5e ?

    • one year ago
  19. Asylum15
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    Why is the 5e on the first line a -?

    • one year ago
  20. mark_o.
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    hmm do it like this 5e^-4t -3e^-2t =5e^-4t D(-4t) -3e^-2tD-2t) =5(-4)e^-4t -3(-2)e^-2t =-20e^-4t +6e^-2t

    • one year ago
  21. Asylum15
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    If you have -3e^-2t and the -2 comes down, wont you have +2 multiplying by -3 = -6? :D

    • one year ago
  22. mark_o.
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    its -3(-2)=+6

    • one year ago
  23. Asylum15
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    Oh :D

    • one year ago
  24. mark_o.
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    but for +3(-2)=-6

    • one year ago
  25. Asylum15
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    Sorry, so now do the 2nd derivative of this?

    • one year ago
  26. mark_o.
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    yeah try that

    • one year ago
  27. Asylum15
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    Any ideas how to start it? Aren't we back where we started?

    • one year ago
  28. Asylum15
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    I need to get an a/b no?

    • one year ago
  29. mark_o.
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    if y'=-20e^-4t +6e^-2t what is y" ?

    • one year ago
  30. mark_o.
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    or for example if y=-20e^-4t +6e^-2t what is dy/dx?

    • one year ago
  31. Asylum15
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    I know i have to derive that. But not sure how to start

    • one year ago
  32. Asylum15
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    Do you use the same rule again?

    • one year ago
  33. mark_o.
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    do the same thing as you did on the first one

    • one year ago
  34. Asylum15
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    ah

    • one year ago
  35. mark_o.
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    yup the same rule applies to it

    • one year ago
  36. Asylum15
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    80e^-4t - 12e^-2t

    • one year ago
  37. mark_o.
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    yeah correct :D now do some multiplication and addition or subtraction using the formula to prove the one you wrote down above the d^2y/dx^2

    • one year ago
  38. Asylum15
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    ? Don't know what you mean

    • one year ago
  39. mark_o.
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    just plug in the one you just solve to the formula d^2y/dt^2 +6 dy/dt +8y =0 _________ +6(_______) +8(________) =0

    • one year ago
  40. mark_o.
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    _________ +6(_______) +8(________) =? solve it and see if you will get zero

    • one year ago
  41. Asylum15
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    But Don't i have a t?

    • one year ago
  42. mark_o.
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    its like 6 dy/dt 6( -20 e^-4t -3e^-2t ) multiply it

    • one year ago
  43. Asylum15
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    Sorry this is taking so long, I got A in my last 3 engineering differentiation exams, but just not getting this one

    • one year ago
  44. Asylum15
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    But how can you say it's equal to zero if you have T and Y still in the equation?

    • one year ago
  45. mark_o.
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    6 dy/dt =6( -20 e^-4t -3e^-2t )= -120 e^-4t -18 e^-2t

    • one year ago
  46. mark_o.
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    you will add or subtract like terms like 100 e^ 7t + 50 e^ 7t = 150 e^ 7t

    • one year ago
  47. Asylum15
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    But T has no value, no given value, so I can't say for example 80^-4t = 0!?

    • one year ago
  48. Asylum15
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    I don't know T! :P

    • one year ago
  49. Asylum15
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    Using your method I have : -40e^-4t + 24e^-2t + 8y = 0

    • one year ago
  50. mark_o.
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    yup it has no value its like this 10 e^ 7t - 10 e^ 7t = 0 e^ 7t=0

    • one year ago
  51. mark_o.
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    just plug in the one you just solve to the formula d^2y/dt^2 +6 dy/dt + 8y =? I I I V V V <------- arrow down pointing it solve them (_____________)+ 6(_________) + 8(_______)= __________ 0 ?

    • one year ago
  52. Asylum15
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    -40e^-4t + 24e^-2t + 8y = 0

    • one year ago
  53. Asylum15
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    :D

    • one year ago
  54. mark_o.
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    d^2y/dt^2 +6 dy/dt + 8y =? (80e^-4t - 12e^-2t) +6(-20e^-4t +6e^-2t) + 8( 5e^-4t -3e^-2t)=?

    • one year ago
  55. mark_o.
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    d^2y/dt^2 + 6 dy/dt + 8y =? (80e^-4t - 12e^-2t) + 6(-20e^-4t +6e^-2t) + 8( 5e^-4t -3e^-2t)=? solve by multiplying first the 6 times the value of dy/dt also 8 times the value of y then add or subtract like terms

    • one year ago
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