Let z be a real number. Find all solutions of the following integral equation: \(f(x)=e^x+z \int_0^1 e^{x-y} f(y)\,dy\) for 0≤x≤1.
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2010-11 Integral Equation,
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Let z be a real number. Find all solutions of the following integral equation: \(f(x)=e^x+z \int_0^1 e^{x-y} f(y)\,dy\) for 0≤x≤1.