The solution of the second-order differential equation $\dfrac{d^{2}y}{dx^{2}}+2\dfrac{dy}{dx}+y=0$ with boundary conditions $y\left ( 0 \right )=1$ and $y\left ( 1 \right )=3$ is

$e^{-x}+\left ( 3e-1 \right )xe^{-x}$

$e^{-x}-\left ( 3e-1 \right )xe^{-x}$

$e^{-x}+\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) -1\right ]xe^{-x}$

$e^{-x}-\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) -1\right ]xe^{-x}$