Verify that the two-dimensional flow given in Cartesian coordinates by

$$\mathbf{u}=\left(\mathrm{e}^{y} \sinh x,-\mathrm{e}^{y} \cosh x\right)$$

satisfies $\nabla \cdot \mathbf{u}=0$. Find the stream function $\psi(x, y)$. Sketch the streamlines.