$\dfrac{dY}{dx}=Y$, where $Y=\begin{pmatrix}y_1(x) \\ y_2(x)\end{pmatrix}$. Also, $Y(0)=\begin{pmatrix} 0\\ 1\end{pmatrix}$.
Then both solutions $y_1(x)$ and $y_2(x)$ are
- increasing functions
- decreasing functions
- neither increasing nor decreasing
- constant functions.
After solving, I got $y_1(x)=A \exp(x)$, $y_2(x)=B \exp(x)$. Boundary conditions give $y_1(x)= 0$ and $y_2(x)=\exp(x)$. The 4th option is incorrect but can not select any option out of remaining three. Please help me.