Which one is the solution $y(x)$ for the following ordinary differential equation and the specified boundary conditions?
\[
\frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+2 y=2 e^{-x} ; y(0)=2 ; \quad\left(\frac{d y}{d x}\right)_{x=0}=1
\]
- $y(x)=\frac{1}{3} e^{-x}-2 e^{x}-\frac{1}{3} e^{2 x}$
- $y(x)=\frac{1}{3} e^{x}+2 e^{x}-\frac{1}{3} e^{2 x}$
- $y(x)=\frac{1}{3} e^{-x}+2 e^{-x}-\frac{1}{3} e^{2 x}$
- $y(x)=\frac{1}{3} e^{-x}+2 e^{x}-\frac{1}{3} e^{2 x}$
