I'm trying to solve this homogeneous Fredholm integral equation of the second kind for $y(x)$.
$y(x) = \int^{\infty}_{-\infty} \ln \left( \frac{1}{x-t} \right) y(t) dt$
I'm aware of Liouville-Neumann series expansions but I cannot find anything online that covers any method for homogeneous equations. The methods & tutorials I have read seem to only cover the inhomogeneous variety, namely:
$y(x) = \int^{\infty}_{-\infty} \ln \left( \frac{1}{x-t} \right) y(t) dt + f(x)$
Either my equation is unsolvable, its solution is somehow implied within its inhomogeneous counterpart, or I've just missed something. I have found a possible solution at https://mathworld.wolfram.com/FredholmIntegralEquationoftheSecondKind.html (Equation 2) but cannot tell what $F(t)$ represents.
Could anyone please help point me towards a solution?