JEE Math Practice Question

Let y = y(x) be the solution of the differential equation $${{dy} \over {dx}} + 2y = f\left( x \right),$$ where $$f\left( x \right) = \left\{ {\begin{matrix} {1,} & {x \in \left[ {0,1} \right]} \\ {0,} & {otherwise} \\ \end{matrix} } \right.$$ If y(0) = 0, then $$y\left( {{3 \over 2}} \right)$$ is :

1. A.$${{{e^2} + 1} \over {2{e^4}}}$$
2. B.$${1 \over {2e}}$$
3. C.$${{{e^2} - 1} \over {{e^3}}}$$
4. D.$${{{e^2} - 1} \over {2{e^3}}}$$