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Today's calculation of Integral 715

Source: 1978 Shibaura Institute of Technology entrance exam

June 25, 2011
calculusintegrationfunctioncalculus computations

Problem Statement

Find the differentiable function f(x)f(x) with f(0)≠0f(0)\neq 0 satisfying f(x+y)=f(x)f′(y)+f′(x)f(y)f(x+y)=f(x)f'(y)+f'(x)f(y) for all real numbers x, yx,\ y.
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