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Implicit differentiation

  1. May 6, 2008 #1
    1. The problem statement, all variables and given/known data
    If dy/dx=xy^2 and x=1 when y=1, then y=

    (A) x^2
    (B) -2/(x^2 -3)
    (C) x^2 + 3
    (D) 2/(x^2 +1)
    (E) (x^2 -3)/2


    2. Relevant equations



    3. The attempt at a solution

    dy/dx=xy^2
    dy=xy^2dx
    dy/y^2=x dx
    ∫dy/y^2=∫x dx
    -1/y = x^2/2 + C
    y=-2/x^2 + C
    1=-2/1^2 + C
    C=3
    y=-2/x^2 +3

    but thats not the answer...

    please help i have the AP test tomorrow.
    thanks
    much appreciated
     
  2. jcsd
  3. May 6, 2008 #2

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    Watch the step between line 5 and 6. f(x) = x^-1 is not linear.
     
  4. May 6, 2008 #3
    That's not really implicit differentiation -- it's a diff. eq.
     
  5. May 6, 2008 #4
    yes?

    when i integrate, it's y^-1/-1 right? not just y^-1
    ??
     
  6. May 6, 2008 #5
    Nevermind I got it.
    Answer is B :)
     
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