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
x+2y \\ 2x-y
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
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.
for the detail.