How to plot a phase portrait for system of differential equations in mathematica or R? Please, help me. I'd like the phase portrait for this system: !enter image description here If anyone can make this portrait and post a print screen here, I would thank you very much.

Online and free (but using neither Mathematica nor R), the code

$$\texttt{streamplot{{-2x*ln(x/y),-y+5sqrt(xy)-3yx^(2/3)},{x,0,5},{y,0,5}}}$$ produces the diagram:

!enter image description here

The fixed point in the middle is a stable node (sink), it might attract every trajectory starting from some $V(0)>0$, $K(0)>0$, and it is located at $$\left(\frac8{3\sqrt3},\frac8{3\sqrt3}\right)\approx(1.5396,1.5396).$$