The problem occurs to me when I tried to solve \begin{align}E(x)=1+2(1-x)^2\int_{x}^{1}(1-t)E\left(\frac{x}{t}\right)dt\end{align} with $E(1)=1$ and $\lim_{x\to 0^+}E(x) \to +\infty$.
I'd like to find $E(1/2)$.
But I have no idea how to solve it with Mathematica or Matlab.
Thank you for your attention!
For Mathematica, you could try to apply the fixed-point and interpolation technique in this article:
http://www.mathematica-journal.com/issue/v9i2/IntegralEquations.html