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Homework Help: Differential Equations - separable?

  1. Apr 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the general solution, y

    2ty dy/dt = 3y^2 - t^2

    2. Relevant equations

    3. The attempt at a solution

    I probably have to separate the equation and get y's one side in order to solve, but I'm stuck as to how to separate it. I tried letting u = y/t, so then

    du/dt = (t dy/dt - y)/(t^2)
    then dy/dt = t du/dt + u , so I plugged it back into the equation?

    t du/dt + u = (3y^2 - t^2)/(2ty)
    t du/dt + u = (3/2)u - (1/2u)

    I can separate this into:
    (u/(u^2-1)) du/dt = 1/2t

    Am I on the right track?
    Last edited: Apr 6, 2009
  2. jcsd
  3. Apr 6, 2009 #2
    Looks like your last line separates to
    (u/(u^2-1))du = dt/(2t)
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