Solve the following set of differential equations (using eigenvalues and eigenvectors) where u is a vector of dimension 2.

$\displaystyle \displaystyle \frac{du}{dt}=\left[ \begin{array}{cc} 1 & 0 \\ 1 & 1 \end{array} \right]u$

My attempt:The eigenvalues of A are 1, 1. $\displaystyle \displaystyle \left[ \begin{array}{c} 0 \\ 1 \end{array} \right]$ is the only eigenvector. How do I proceed?