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For `x in R, x != 0` if `y(x)` is a differentiable function such that `x int_(1)^(x)y(t)dt = (x+1) int_(1)^(x)ty(t)dt`, then `y(x)` equals (where C is a constant)

A

`Cx^(3)e^(1/x)`

B

`C/(x^(2))e^(-1/x)`

C

`C/xe^(-1/x)`

D

`C/(x^(3))e^(-1/x)`

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The correct Answer is:
D
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