1.

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:

Answer»

4
3
5
2

Solution :`F(xy) = f(x).f(y)`
`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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