1.

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.)

Answer»

`C a^(3) 1/e^(x)`
`(C)/(x^(2))e^(1/x)`
`(C)/(x) e^(- 1/x)`
`(C)/(x^(3))e^(- 1/x)`

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