First-Order Nonlinear ODE from transient heat transfer

[mafra]

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:
http://www.wolframalpha.com/input/?i=T'(t)+=+a+-+b*T(t)+-+c*T(t)^4

Could anyone give me some light here?

 

[JJacquelin]

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)

 

[mafra]

Thanks mate! That's simpler than I thought. So problably he was referring to an analytical solution for T(t)