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Homework Help: Which of the Following is a solution to the differential Equation

  1. Feb 9, 2013 #1
    1. The problem statement, all variables and given/known data
    Which fot he following is a solution to the differential equation:

    t2y" - 2ty' + 2y = 0

    a)e-2tt3

    b)et

    c)t

    d) t4

    I have attached an image of the question

    2. Relevant equations



    3. The attempt at a solution

    I tried answer d first:

    y = t4

    y' = 4t3

    y" = 12t2

    Plugging in these derivatives:

    t2(12t2) - 2t(4t3) + 2(t4) = 0

    I also checked with y = t and this solution works as well. So how do I distinguish between which one is the correct answer?
     

    Attached Files:

  2. jcsd
  3. Feb 9, 2013 #2
    \neq
    I think you just made an arithmetic mistake ;)
    [tex] t^2(12t^2) - 2t(4t^3) + 2(t^4) = 12t^4 - 8t^4 + 2t^4 = 6t^4 \neq 0[/tex]

    In many cases, DE's can have multiple different solutions.
     
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