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Differential Equations: If y(1) =3 then y(1/2) = ?

  1. Feb 10, 2013 #1
    1. The problem statement, all variables and given/known data
    If y satisfies the differential equation:

    ty'(t) + tln(t)y(t) = 0

    and y(1) = 3 then y(1/2) = ?

    I have attached an image of the question with the possible solutions:


    2. Relevant equations



    3. The attempt at a solution

    Initially I tried plugging in t=1 and y(1) = 3 giving me:

    y'(1)+3ln(1) = 0

    Hence y'(1) = 0

    I did the same for t=1/2

    1/2[y'(1/2) + ln(1/2)y(1/2)] = 0

    But this doesn't seem to help me. Any suggestions would be appreciated.
     

    Attached Files:

  2. jcsd
  3. Feb 10, 2013 #2

    LCKurtz

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    Why don't you just solve the DE and put in the boundary conditions? It looks to be separable and linear so you have a couple of options.
     
  4. Feb 10, 2013 #3

    SammyS

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    To help you solve the D.E., factor out t .
     
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