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Differentiation question with continuity

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose a function f is continuous and has continuous derivatives of all orders for all
    x. it satisfies xf ''(x) + f '(x) + xf(x) = 0. Given f(0) = 1

    find the value of f '(0) and f '' (0).

    2. Relevant equations



    3. The attempt at a solution

    when x=0,

    0f''(0) + f ' (0) + 0f(0) = 0
    therefore f ' (0) = 0

    Now, I am not sure on how to find f ''(0). Is it undefined?
    Thanks for your help.
     
    Last edited: Mar 28, 2012
  2. jcsd
  3. Mar 28, 2012 #2

    Dick

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    There's no attempt at a solution. You have to make one. Then you can get some help.
     
  4. Mar 28, 2012 #3
    I have added the solution attempt, please help. Thanks :)
     
  5. Mar 28, 2012 #4

    Dick

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    That helps. Try differentiating xf ''(x) + f '(x) + xf(x) = 0 and putting x=0 again.
     
  6. Mar 28, 2012 #5
    Wow. Thanks Dick! :D
     
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