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anonymous

  • 5 years ago

(d^2y/dx^2) of (dy/dx)=y^2(6-2x)

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  1. amistre64
    • 5 years ago
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    you want the derivative of the derivative :)

  2. anonymous
    • 5 years ago
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    how do i do that!

  3. amistre64
    • 5 years ago
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    or the 3rd derivative..... hard to tell

  4. amistre64
    • 5 years ago
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    implicit or solve for y

  5. amistre64
    • 5 years ago
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    implicits.....

  6. anonymous
    • 5 years ago
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    i dont know what d^2y/dx^2 means

  7. amistre64
    • 5 years ago
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    d^2y/dx^2 is just the 2nd derivative of an equation, for example: y = 2x^2 dy/dx = 4x d2y/dx2 = 4

  8. anonymous
    • 5 years ago
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    oh, so i am just finding the 3rd derivative pretty much?

  9. amistre64
    • 5 years ago
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    thats what I think..... and youll have to use implicit stuff y'=y^2(6-2x)

  10. anonymous
    • 5 years ago
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    I forgot what implicits are):

  11. amistre64
    • 5 years ago
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    implicits are the same steps as normal derivatives except you "keep" the implicits in the equation to factor out in the end...like this: x+xy = 4 d(x) + d(xy) = d(4) dx + dx y + x dy = 0 solve for dy

  12. amistre64
    • 5 years ago
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    dy = -dx -dx y//x ; dx = 1 so.. dy = -1 -y //x

  13. amistre64
    • 5 years ago
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    y' = y^2(6-2x) y'' = y' 2y(6-2x) + y^2(-2x)x' ; x' = 1 y'' = y' 12y -4xy - 2xy^2 is what I get

  14. anonymous
    • 5 years ago
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    how do i find the derivative of y, like x's you bring the exponent to the front? like if it says y^2 what do i do?

  15. amistre64
    • 5 years ago
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    watch what we do with derivatives :) d (2x^3) dx (6x^2) ---- = ---- dx dx now dx/dx = 1 usually so we omit it.... right?

  16. amistre64
    • 5 years ago
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    d (y^2) dy (2y) ---- = ---- dx dx dy/dx IS y' or the first derivative. it doesnt cancel so we just keep it in the equation as y'

  17. anonymous
    • 5 years ago
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    so it will be 2y y' ?

  18. amistre64
    • 5 years ago
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    thats absolutely correct :)

  19. amistre64
    • 5 years ago
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    after your done ; substitute the value for y' into the finished work

  20. anonymous
    • 5 years ago
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    so if i do this problem y^2(6-x) i have to do 2y y'(6-2x)(-2)?

  21. amistre64
    • 5 years ago
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    i find it ironic that they title me "superhero", and your named "helpless" lol

  22. anonymous
    • 5 years ago
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    Hahaha, that is funny!

  23. amistre64
    • 5 years ago
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    y^2(6-x) is simply the product rule with a little extra stuff jambed between the lines....

  24. amistre64
    • 5 years ago
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    rl' + r'l is all it amounts to

  25. amistre64
    • 5 years ago
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    r = y^2 r' = y' 2y l = (6-x) l' = -1

  26. anonymous
    • 5 years ago
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    oh! so it'll be 2y y'(6-2x)+y^2(-2)? or am i going off on the wrong track with the y's again?

  27. amistre64
    • 5 years ago
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    squish it all together and simplify

  28. anonymous
    • 5 years ago
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    sorry the problem was actually y^2(6-2x)

  29. amistre64
    • 5 years ago
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    yes.... i missed the 2 from up top...but yes...thats it

  30. amistre64
    • 5 years ago
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    you already know what y' equals, it was the original problem right?

  31. amistre64
    • 5 years ago
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    I think they ask for y'' and give you y'=yadayada..... so this would be the final step :)

  32. anonymous
    • 5 years ago
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    No y'=y^2(6-2x) so then 2y y'(6-2x)+y^2(-2) is y"

  33. anonymous
    • 5 years ago
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    so i just leave it like that?

  34. amistre64
    • 5 years ago
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    you can...but just be aware that any answers on a test might be written in the full expanded form.

  35. anonymous
    • 5 years ago
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    how would i do that?

  36. amistre64
    • 5 years ago
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    just replace the y' with y^2(6-2x) and work the math :) 2y (y^2)(6-2x)(6-2x)+y^2(-2)

  37. amistre64
    • 5 years ago
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    2y^3(36-24x +4x^2) -2y^2

  38. amistre64
    • 5 years ago
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    and so on and so forth...

  39. anonymous
    • 5 years ago
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    how'd you get this part?

  40. amistre64
    • 5 years ago
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    lets step thru this... we found y'' right? what is it?

  41. anonymous
    • 5 years ago
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    nevermind i think i get it because you did (6-2x)(6-2x) to get (36-24x +4x^2)

  42. amistre64
    • 5 years ago
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    yes... :)

  43. amistre64
    • 5 years ago
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    y' was the only variable we new the "value" of, so I just replaced it and did the math

  44. anonymous
    • 5 years ago
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    '& that's the answer right? So if it gives me a point, i would just plug the values in for my x and y? then solve for that?

  45. amistre64
    • 5 years ago
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    thats right, with implicits they have to give you a way to know the x and y values.....

  46. anonymous
    • 5 years ago
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    okay i think i got it. But part b says to find y=f(x) by solving (dy/dx)=y^2(6-2x) using the initial condition f(3)+1/4

  47. anonymous
    • 5 years ago
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    *f(3)=1/4

  48. amistre64
    • 5 years ago
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    you gotta di the inegral to find F(x) ;)

  49. anonymous
    • 5 years ago
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    so i do the anti derivative of y'?

  50. amistre64
    • 5 years ago
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    jsut "cross multiply" to split the variables...... yeah

  51. amistre64
    • 5 years ago
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    dy y^2(6-2x) --- = --------- dx 1

  52. amistre64
    • 5 years ago
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    [S] 1/(y^2) dy = [S] 6-2x dx

  53. anonymous
    • 5 years ago
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    whats [S] ?

  54. amistre64
    • 5 years ago
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    its my lazy version of the elongfated "S" symbol they use for the integral/anti derivative stuff

  55. amistre64
    • 5 years ago
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    \[\int\limits_{}\]

  56. anonymous
    • 5 years ago
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    ohhhhhh!

  57. amistre64
    • 5 years ago
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    i loathe the "equation" editor, slows down the computer with it trying to decode all the stuff

  58. anonymous
    • 5 years ago
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    Hahahahah, i get you!(: how did you get that from cross multiplying though?

  59. anonymous
    • 5 years ago
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    you seperated them?

  60. amistre64
    • 5 years ago
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    this is our original problem right? dy y^2(6-2x) --- = --------- dx 1 we cross multiply to get the "y" stuff to one side and the "x" stuff to the other so we can inegrate them separately

  61. amistre64
    • 5 years ago
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    if you havent read ahead past the "antiderivative" jargon yet... then you probably are wondering if I can do that :)

  62. anonymous
    • 5 years ago
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    Okay so when once i get them separated, is 1/y^2 lny^2?

  63. amistre64
    • 5 years ago
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    now now..make it easier on yourself...1/y^2 = y^-2

  64. amistre64
    • 5 years ago
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    [S] y^-2 dy = [S] (6-2x) dx

  65. amistre64
    • 5 years ago
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    y^-1/-1 = 6x -(2)x^2/2 + C

  66. amistre64
    • 5 years ago
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    -1/y = -x^2 +6x + C

  67. anonymous
    • 5 years ago
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    why is it -2x^2/2 why is it divided by two and not just x^2?

  68. amistre64
    • 5 years ago
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    .... its a place holder so I dont lose track of it and make more mistakes than ususal :) -2x becomes -2x^2/2 simplify .... -x^2

  69. amistre64
    • 5 years ago
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    tuen each side of..to the reciprocals.. to get "y" on top

  70. amistre64
    • 5 years ago
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    -y = 1 // -x^2 +6x + C get rid of the (-) by dividing both sides by -1 y = 1 // x^2 -6x - C and we should have it

  71. amistre64
    • 5 years ago
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    i took typing class and passed....honest :)

  72. anonymous
    • 5 years ago
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    what does the // mean? sorry, i dont know how to do all this math anywhere but on paper.

  73. amistre64
    • 5 years ago
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    I use that to mean the there is a larger fraction bar that separates the top and bottom, it just means that everything before it is on top and everything after it is on bottom. otherwise id look like this: 1/x^2 -6x -C which can be misleading....

  74. amistre64
    • 5 years ago
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    plug in your inital values and lets solve for "C" :)

  75. anonymous
    • 5 years ago
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    so is it 1/4=(1/(x2-6x+c))

  76. anonymous
    • 5 years ago
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    if the i.c is f(3)+.25

  77. anonymous
    • 5 years ago
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    f(3)=.25

  78. amistre64
    • 5 years ago
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    x^2 -6x +C = 4 x^2 -6x -4 = C right?

  79. amistre64
    • 5 years ago
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    x = 3 and y = 1/4 yes

  80. anonymous
    • 5 years ago
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    right.

  81. amistre64
    • 5 years ago
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    9 - 18 - 4 = C C = -13 if I did it right :)

  82. anonymous
    • 5 years ago
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    where is the 4 coming form?

  83. amistre64
    • 5 years ago
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    lets see if: it works for us :) 1/4 = 1/(9 -18 -13) ...you put it there with the 1/4......right?

  84. amistre64
    • 5 years ago
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    4 = 3^2 -6(3) + C

  85. anonymous
    • 5 years ago
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    okay waitso the equation is 1/4=(1/(x^2-6x+c)?

  86. amistre64
    • 5 years ago
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    yep, cross multiply or jsut flip them both over or jsut notice that the bottom parts need to match up and equal each other

  87. anonymous
    • 5 years ago
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    okay so when i plug in the point i get 1/4=9-18+c?

  88. amistre64
    • 5 years ago
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    no...lets start at the beginning of this: 1 y = ----------- x^2 -6x +C f(3) = .25 = 1/4 1 1 -- = -------------- 4 (3)^2 -6(3) +C 4 = 9 -18 + C

  89. anonymous
    • 5 years ago
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    so because 1 is on top on both sides i can cancel it?

  90. amistre64
    • 5 years ago
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    ....not "because" the 1 is on top..... but yeah. we are wanting to make that bottom right hand side the same number as the bottom of the left hand side. We can either cross multiply and get them both on top. We can flip them over to their reciprocal counterparts (which is what I did). Or, we can simply notice that the only thing that matters in this equation is that the bottom numbers have to equal and we can ignore anything else :)

  91. anonymous
    • 5 years ago
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    Okay i got it now. Now i see how you got C=13 (:

  92. amistre64
    • 5 years ago
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    .... lol good :)

  93. anonymous
    • 5 years ago
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    okay! Thank you so much!:D

  94. amistre64
    • 5 years ago
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    did we solve our problem? because I am wondering if that +C changes if we are looking for -C.... better get 2 answers so you can double check yourself

  95. anonymous
    • 5 years ago
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    wait how do i find -C?

  96. amistre64
    • 5 years ago
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    just change +C to -C and get an answer for it.....

  97. anonymous
    • 5 years ago
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    wouldnt it just be -13?

  98. amistre64
    • 5 years ago
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    dunno, my brains not giving me an answer lol 4 = 9 -18 - C C = 9-4-18 C = 5 - 18 = -13 were good.....

  99. anonymous
    • 5 years ago
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    so i put plus and minus 13 as my answer and my problem is completely answered?(:

  100. amistre64
    • 5 years ago
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    +c = 13 -c = --13 = 13 c = 13

  101. anonymous
    • 5 years ago
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    okay got it! Thank you for your help!(:

  102. amistre64
    • 5 years ago
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    youre welcome :)

  103. anonymous
    • 5 years ago
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    I might be back tomorrow, hahahah.(;

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