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Let f:(0,oo)->R be a differentiable func...

Let `f:(0,oo)->R` be a differentiable function such that `f'(x)=2-f(x)/x` for all `x in (0,oo)` and `f(1)=1`, then f(x) is

A

`(3)/(1+9x^(3))`

B

`(9)/(1+9x^(3))`

C

`(3xsqrt(x))/(1-9x^(3))`

D

`(3x)/(1-9x^(3))`

Text Solution

AI Generated Solution

To solve the problem, we start with the given differential equation and the initial condition. ### Step 1: Write down the differential equation We are given: \[ f'(x) = 2 - \frac{f(x)}{x} \] and the initial condition: ...
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