# Solution of the Fredholm equation f(x)=int_0^1 2*x*y/(x+y) f(y) dy

• May 11th 2012, 05:48 AM
AlexisM
Solution of the Fredholm equation f(x)=int_0^1 2*x*y/(x+y) f(y) dy
Hi,

I was wondering if there were known solutions to the following homogeneous Fredholm integral equation:
$f(x) = \int_0^1 \frac{2xy}{x+y} f(y) dy$

And more generally to:

$f(x) = \int_0^1 \sqrt{xy}\phi(\log(\frac{y}{x})) f(y) dy$
where $\phi(x)$ is a symmetric function.