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Integral Eq Fredholm Method

dwsmith

Well-known member
Feb 1, 2012
1,673
How does one use the Fredholm Method when we have a sum of separable kernels?
\[
f(x) = 1 + \lambda\int_0^1(xy + x^3y^2)f(y)dy
\]
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?