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Black Book Advanced Problems in MathematicsMathematicsDifferential Equations

Let f(x) be a differentiable function in [-1, ) and f(0) = 1 such that _ t x+1 t^2 f(x+1) - (x+1)^2 f(t) f(t) - f(x+1) = 1 . Find the value of _ x 1 (f(x)) - 2 x-1 .

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