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.