A) 2
B) 2e
C) e
D) 0
Correct Answer: A
Solution :
Given\[\frac{dy}{dx}+\left( \frac{1}{2\log x} \right)y=2\] I.F. \[={{e}^{\int_{{}}^{{}}{\frac{1}{x\log x}dx}}}\] \[={{e}^{\ell n(\ell nx)}}\] \[=\ell nx\] \[\therefore \]soln. is \[y\left( \ell nx \right)=\int_{{}}^{{}}{2\ell nx}dx+C\] \[y\left( \ell nx \right)=2x(\ell nx-1)+C\] ?(1) Given\[x\ge 1\] At x = 1 \[y(0)=-2+C\] \[\Rightarrow \]\[C=2\] Sol in (1) \[y(\ell nx)=2x(\ell nx-1)+2\] \[\therefore \]put x = e, \[y=2(0)+2\] \[\]
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