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Fredholm equation with non-seperable kernel

equation

I'm trying to solve this form of Fredholm equation. where, vinit, vth, vstep, vleak is a constant and f1 description

Are there any method or theorm that can solve this problem?

Since I'm freshman in university, it's very challenging for me. But I really want to untangle this problem.

Can you help me to solve this kind of equation or let me know what theory I should start with?

I would be grateful if you could just give me directions, so I can know where to start studying. Sorry for my bad English.