General solution of (d^2 y)/(d x^2)=e^-2 x is :

$\frac{d^2 y}{d x^2}=e^{-2 x}, \frac{d y}{d x}=\frac{e^{-2 x}}{2}+k_1$

Integrating, $y=\frac{e^{-2 x}}{4}+k_1 x+k_2 \Rightarrow y=\frac{e^{-2 x}}{4}+cx+d$

Hence (3) is the correct answer.