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Let f: [0,1] to R be such that f(xy). F(y) AA x, y in (0,1) and f(0) != 0. If y = y(x) satisfies the differential equation, (dy)/(dx) = f(x) with y(9) = 1 they y((1)/(5))+y((4)/(5)) is equal to: |
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Answer» 4 `f(o) = 1 as f(o) != 0 implies f(x) =1` `(DY)/(DX) = f(x) = 1 implies y = x + C` At `x = 0, y = 1 implies c = 1 implies y = x +1` `implies y((1)/(5)) + y((4)/(5)) = 1/5 + 1 + 4/5 + 1 = (1+1+1) = 3`. |
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