Find two linearly independent solutions of

$$y^{\prime \prime}+4 y^{\prime}+4 y=0 .$$

Find the solution in $x \geqslant 0$ of

$$y^{\prime \prime}+4 y^{\prime}+4 y=e^{-2 x},$$

subject to $y=y^{\prime}=0$ at $x=0$.