## The two-dimensional steady incompressible irrotational fluid flow

In the present page we numerically solve the $$2\times2$$ system of ordinary differential equations of the form $\frac{d}{dt} \begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} x+2y \\ 2x-y \end{bmatrix}.$ The solutions to this system are the integral curves of the planar vector field $$(x+2y,2x-y)$$ in the $$xy$$-plane. In terms of classical mechanics solutions to this system describes the streamline of the two-dimensional steady incompressible irrotational fluid flow given by a complex velocity potential $W(z) = \frac{(1-2i)z^2}{2}, \quad z=x+iy.$ In this case the streamlines coinside with both streaklines and particle paths since the flow is steady.
By using MATLAB we draw the vector field amd its integral curves. See fluid_flow.m for the detail.