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anonymous

  • 4 years ago

how do you solve the initial value problem of 4y(3)+2y=0;y(0)=2y(0)=5y(0)=6

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  1. anonymous
    • 4 years ago
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    i got the wrong answer :(

  2. anonymous
    • 4 years ago
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    Can you retype the question? It didn't come out right? What are those 0s? Are they exponents or numbers?

  3. anonymous
    • 4 years ago
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    they are numbers

  4. anonymous
    • 4 years ago
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    But they are 0s?

  5. lalaly
    • 4 years ago
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    What course are studying?

  6. anonymous
    • 4 years ago
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    Here's is the problem again: 4y'''+2y''=0 y(0)=2 y'(0)=5 y''(0)=6

  7. anonymous
    • 4 years ago
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    yes they are zeros

  8. anonymous
    • 4 years ago
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    calc?

  9. lalaly
    • 4 years ago
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    differential eqns:D

  10. anonymous
    • 4 years ago
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    and im taking differential equations

  11. anonymous
    • 4 years ago
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    yes lol

  12. anonymous
    • 4 years ago
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    the 3 in the problem represents the third derivative im sorry the original post looks weird

  13. anonymous
    • 4 years ago
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    its supposed to be 4y'''+2y''=0 as in to the third derivative and the second derivative

  14. lalaly
    • 4 years ago
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    \[4r^3+2r^2=0\]\[2r^2(r+2)=0\]\[r=0,0,-1/2\]so \[y=c_1e^{-0.5x}+c_2x+c3\]

  15. lalaly
    • 4 years ago
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    \[y'=-0.5c_1e^{-0.5x}+c_2\]

  16. lalaly
    • 4 years ago
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    \[y''=0.25c_1e^{-0.5x}\]

  17. anonymous
    • 4 years ago
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    yes i got that but i think i did something wrong after that

  18. lalaly
    • 4 years ago
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    just plug in the values of x and y, nothing'd go wrong

  19. anonymous
    • 4 years ago
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    i did but the answer is wrong! i did y(0)=2=c_1 +c_3

  20. anonymous
    • 4 years ago
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    y'(0)=5=c2-(1/2)c3e^(-1/2x)

  21. lalaly
    • 4 years ago
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    no the e part cancels coz it equals 1 when x =0

  22. lalaly
    • 4 years ago
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    y'(0)=c2-1/2c3

  23. anonymous
    • 4 years ago
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    yea i know and thats how i solved for c2=12

  24. lalaly
    • 4 years ago
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    wait let me do it

  25. lalaly
    • 4 years ago
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    \[y(0)=2\]\[c_1+c_3=2\] \[y'(0)=5\]\[-0.5c_1+c_2=5\] \[y''(0)=6\]\[0.25c_1=6\]\[c_1=24\] \[24+c_3=2\]\[c_3=-22\]\[-0.5(24)+c_2=5\]\[c_2=17\]

  26. anonymous
    • 4 years ago
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    I got c2=-7 and thats where i went wrong! thanks soooo much!

  27. lalaly
    • 4 years ago
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    :D:D its ok, its confusing i know lol, ur welcome

  28. anonymous
    • 4 years ago
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    i frogot .5 was negative

  29. anonymous
    • 4 years ago
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    Thanks again! :)

  30. lalaly
    • 4 years ago
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    anytime:)

  31. anonymous
    • 4 years ago
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    can I ask another question?

  32. lalaly
    • 4 years ago
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    sure:D

  33. anonymous
    • 4 years ago
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    8y''+4y'+4y=0, where y(0)=4 and y'(0)=1

  34. lalaly
    • 4 years ago
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    u want the answers or the whole solution?

  35. anonymous
    • 4 years ago
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    the solution please

  36. anonymous
    • 4 years ago
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    but if you cant you can give the answer and I can try to work backwards

  37. lalaly
    • 4 years ago
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    ok give me 5 min let me work it out

  38. anonymous
    • 4 years ago
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    thanks sooooo much

  39. lalaly
    • 4 years ago
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    \[y=c_1e^{-\frac{x}{4}}\cos(\frac{\sqrt 7}{4}x)+c_2e^{-\frac{x}{4}}\sin(\frac{\sqrt 7}{4}x)\] i got \[c_1=4\]\[c_2=3.02\]

  40. anonymous
    • 4 years ago
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    ok let me check thanks again

  41. lalaly
    • 4 years ago
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    :):)

  42. anonymous
    • 4 years ago
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    woohoooo its correct! thanks sooo much

  43. lalaly
    • 4 years ago
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    hehe yaaay :D

  44. anonymous
    • 4 years ago
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    ok i have one last question but if you dont want to do it its totally fine! i had a bunch of roblems to do and these were the three i couldnt get so if its ok can i ask you another one? i feel bad for asking!

  45. lalaly
    • 4 years ago
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    lol dont feel bad, id love to help, why else would i be on openstudy

  46. anonymous
    • 4 years ago
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    true lol thanks soo much! here is the question:

  47. anonymous
    • 4 years ago
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    Find a linear homogeneous constant-coefficient differential equation with the general solution: y(x)=c1e^(2x) + c2Cos(9x) +c3Sin(9x) that has the form y'''+_________y''+_____y'+____y=0 the underscores are supposed to represent blanks lol

  48. lalaly
    • 4 years ago
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    i got off here by mistake :S let me do it again

  49. anonymous
    • 4 years ago
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    okie dokes! :)

  50. lalaly
    • 4 years ago
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    the solutions are 2,+/-9i

  51. lalaly
    • 4 years ago
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    so (r-2)(r^2+81)=0

  52. lalaly
    • 4 years ago
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    r^3-2r^2+81r-162=0

  53. lalaly
    • 4 years ago
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    y'''-2y''+81y'-162y=0

  54. anonymous
    • 4 years ago
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    how did you get the solutions?

  55. lalaly
    • 4 years ago
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    do u know how u find the general solution like when u get r=2,3 the general solution is y=c1e^2x+c_2e^3x and when u get complex solutions a+bi and a-bi the general solution is y=e^ax(c1cos(bx)+c2sin(bx)... u just do it back wards

  56. anonymous
    • 4 years ago
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    oh ok I got it! thnkssss sooo much!!! i really appreciate all yr help!! I also noticed that you joioned 3arabi open stidy group! r u taking arabic classes?

  57. anonymous
    • 4 years ago
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    study*

  58. lalaly
    • 4 years ago
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    lol no im half arab :D:D i speak arabic

  59. anonymous
    • 4 years ago
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    oh lol I was going to ask if you need any help because I also speak arabic and it's my minor

  60. lalaly
    • 4 years ago
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    oh wow really :D:D where are u from hehe

  61. anonymous
    • 4 years ago
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    I'm palestinian! hbu?

  62. lalaly
    • 4 years ago
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    o ana kmaaaaaaaaaaaaaan :D

  63. anonymous
    • 4 years ago
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    but if you're referring to city, I'm from Dearborn lol

  64. anonymous
    • 4 years ago
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    omg nooo waaayyy!!! how cool!

  65. lalaly
    • 4 years ago
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    hehe im from hebron hehe

  66. anonymous
    • 4 years ago
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    oh by dearborn i meant city in the US haha I'm from beit safafa in palestine

  67. anonymous
    • 4 years ago
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    do you live in palestine?

  68. lalaly
    • 4 years ago
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    oh lol i dont know abt US lol, ana 3ayshe bi newzealand

  69. anonymous
    • 4 years ago
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    ooooo keef new zealns? keef al; taqs hunak?

  70. anonymous
    • 4 years ago
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    zealand*

  71. lalaly
    • 4 years ago
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    hehe its summer so yaaaaaaaaay !! :D newzealand btjanen bmoot feha hehe, 3njad sodfe helwee:D:D iza bedik more help ask me :D

  72. anonymous
    • 4 years ago
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    3njad inti bit mooti feeha? lol hon it's winter bes ana behab al pelletaa3! bhab al thalj! and shukran bes khalasit wajabatee! thanks soo much! i really appreciate your help!

  73. anonymous
    • 4 years ago
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    i was supposed to say pelletaa3 not pelletaa3 lol i have no idea hot i typed that instead! lol sorry for the confusion

  74. anonymous
    • 4 years ago
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    pelletaaaa3 as in winter* i dont know why it keeps sending it as something else

  75. lalaly
    • 4 years ago
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    if u catch me on here at anytime ill be glad to help u o sara7a u made my day hehe i was a lil upset, bas u made me smile :D hehe Fhemt-ha

  76. anonymous
    • 4 years ago
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    thanks so much! and same to you! if you have any questions I'll be more than glad to help to the best of my ability! and I'm glad to have made your day! a smile is always better than a frown! :)

  77. lalaly
    • 4 years ago
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    hehe nice to meet you, esme lana btw

  78. anonymous
    • 4 years ago
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    nice to meet you lana! ismee Ranya

  79. lalaly
    • 4 years ago
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    oooo kman my favorite name ya salam hehe

  80. anonymous
    • 4 years ago
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    haha shukran!

  81. anonymous
    • 4 years ago
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    btasif bes lazim arooh leana lazam arooh ijeeb igrath min al mahalat! bye! and talk to you soon inshallah! :)Have a great day!! :)

  82. lalaly
    • 4 years ago
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    :D:D okay take care,, bye byee

  83. anonymous
    • 4 years ago
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    bye :)

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