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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!

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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

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Thank you! I have tried the iteration, but when f(x) tends to zero, it's hard to interpolate the function, is there any useful idea to solve this problem? – Golbez Sep 19 '12 at 10:44

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