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\[

f(x) = 1 + \lambda\int_0^1(xy + x^3y^2)f(y)dy

\]

Do we or can we just say \(K(x, y) = xy + x^3y^2\) and proceed normally finding the Fredholm Resolvent? Or do we have to use the sum of separable kernels method with the Fredholm method?

If the answer we have to use the sum of separable kernels method with the Fredholm method, how is this done?