Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Asylum15 Group Title

Differentiation Question! :(

  • one year ago
  • one year ago

  • This Question is Closed
  1. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

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

    • one year ago
  2. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Derive Y?

    • one year ago
  3. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    use the formula D(e^u)= e^u D(u) lets see what will you get

    • one year ago
  4. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So Y' = -4(5e^-4t) + 2 (-3e^-2t) ?

    • one year ago
  5. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    e^ax = ae^ax

    • one year ago
  6. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    De^ax = ae^ax yup

    • one year ago
  7. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So my first step is correct?

    • one year ago
  8. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ah +3

    • one year ago
  9. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[= -4(5e ^{-4t}) + 2(-3e ^{-2t})\]

    • one year ago
  10. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

    • one year ago
  11. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry about that i dint solved it my self but im just guiding you to the right solution :D

    • one year ago
  12. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So am i right so far?

    • one year ago
  13. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes correct :D

    • one year ago
  14. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, what should I do next? :)

    • one year ago
  15. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    now do the 2nd derivative

    • one year ago
  16. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Y'' yeah?

    • one year ago
  17. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yup but you can still simplify that one by multiplying the constant coefficients

    • one year ago
  18. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    -4 multipled by 5e ?

    • one year ago
  19. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Why is the 5e on the first line a -?

    • one year ago
  20. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    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. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    its -3(-2)=+6

    • one year ago
  23. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh :D

    • one year ago
  24. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    but for +3(-2)=-6

    • one year ago
  25. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry, so now do the 2nd derivative of this?

    • one year ago
  26. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah try that

    • one year ago
  27. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Any ideas how to start it? Aren't we back where we started?

    • one year ago
  28. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I need to get an a/b no?

    • one year ago
  29. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    if y'=-20e^-4t +6e^-2t what is y" ?

    • one year ago
  30. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    or for example if y=-20e^-4t +6e^-2t what is dy/dx?

    • one year ago
  31. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I know i have to derive that. But not sure how to start

    • one year ago
  32. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you use the same rule again?

    • one year ago
  33. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    do the same thing as you did on the first one

    • one year ago
  34. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ah

    • one year ago
  35. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yup the same rule applies to it

    • one year ago
  36. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    80e^-4t - 12e^-2t

    • one year ago
  37. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ? Don't know what you mean

    • one year ago
  39. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    _________ +6(_______) +8(________) =? solve it and see if you will get zero

    • one year ago
  41. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    But Don't i have a t?

    • one year ago
  42. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    its like 6 dy/dt 6( -20 e^-4t -3e^-2t ) multiply it

    • one year ago
  43. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    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 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    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. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    6 dy/dt =6( -20 e^-4t -3e^-2t )= -120 e^-4t -18 e^-2t

    • one year ago
  46. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you will add or subtract like terms like 100 e^ 7t + 50 e^ 7t = 150 e^ 7t

    • one year ago
  47. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    But T has no value, no given value, so I can't say for example 80^-4t = 0!?

    • one year ago
  48. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't know T! :P

    • one year ago
  49. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Using your method I have : -40e^-4t + 24e^-2t + 8y = 0

    • one year ago
  50. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yup it has no value its like this 10 e^ 7t - 10 e^ 7t = 0 e^ 7t=0

    • one year ago
  51. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    -40e^-4t + 24e^-2t + 8y = 0

    • one year ago
  53. Asylum15 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    :D

    • one year ago
  54. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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. Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.