I was recently studying about solution of the following homogeneous Fredholm equation of first kind $$x=\lambda\int_0^1e^{x-t}y(t)dt$$ if there's any . But the method of regularization (since the kernel is separable) and homotopic perturbation method both give a rather diverging solution for this problem . So I suspect if any solution exists at all . Is there any other method for any approximate solution to this kind of problem ? If this problem has indeed no solution , then what is the theoretical reason behind it ? Any help is appreciated .
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1Unless I miss something (?) can you not take $e^x$ out of the integral, then note that the integral over $t$ results in a constant $c$ leading to $x=e^x \lambda c$ which cannot have solutions for all $x$ – Sal Nov 14 '21 at 14:19
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Is $x$ meant to be a scalar? Or a function? – Severin Schraven Nov 14 '21 at 23:09