If y(x) is the solution of the differential equation ${{dy} \over {dx}} + \left( {{{2x + 1} \over x}} \right)y = {e^{ - 2x}},\,\,x > 0,\,$ where $y\left( 1 \right) = {1 \over 2}{e^{ - 2}},$ then

Question

y(log_e2) = log_e4

y(x) is decreasing in (0, 1)

y(log_e2) = ${{{{\log }_e}2} \over 4}$

y(x) is decreasing in $\left( {{1 \over 2},1} \right)$

Solution

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