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First-Order Nonlinear ODE from transient heat transfer

  1. Jun 26, 2012 #1
    A problem from a heat transfer book with conduction and radiation led me to a differential equation like this:

    T'(t) = a - b*T(t) - c*T(t)^4

    Although my professor said that there wouldn't be an analytical solution for this one and to get the answer by an iterative method I got curious and tried Wolfram Alpha. For my surprise it gave a solution, but I just can't understand the answer and neither the steps for solving it

    Here it is:

    Could anyone give me some light here?
  2. jcsd
  3. Jun 27, 2012 #2
    The solution is shown in attachment.
    WolframAlpha gives a closed form of the integral in terms of the four roots of the polynomial :
    a - b*T - c*T^4 = c*(T-w1)*(T-w2)*(T-w3)*(T-w4)

    Attached Files:

  4. Jun 27, 2012 #3
    Thanks mate! That's simpler than I thought. So problably he was referring to an analytical solution for T(t)
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