$$\frac{\mathrm{d}x}{\mathrm{d}t}=x(x-y) \quad\text{and}\quad \frac{\mathrm{d}y}{\mathrm{d}t}=y(2x-y)$$
I know that
- A fixed point is $(0,0)$.
- The Jacobian is
$$ \begin{pmatrix} 2x-y & -x \\ 2y & 2x-2y \end{pmatrix}. $$
We can find when the Jacobian becomes
$$ \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix} $$
so that the eigenvalues become $0$ as well.
However, I do not know how to draw the phase portrait.