I need to find a general solution,

∈

for the Fredholm intergral equation:

where is the intergral operator defined by

Where and are postive constants and and ∈ ℝ constants.

I think, that I have to rewrite it:

And then assuming that λ is a fixed unknown scalar, and so can be incorporated into the equation as follows:

I'm not sure if this is right, and I don't really understand what to do next, can someone help please?