What type of integral equation is this and how can I solve it?

muttley78
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I would ask help to solve the following integral equation. Any suggestion? Any references to look at?

f(x)=int_{0}^{x} (A*exp{t-x}+B)f(t)g(t/x)*(1/x)dt

A, B known constant

Thanks a lot.
 
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Thread 'Volterra equation of the second kind'

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
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