```python
import loader
from sympy import *
init_printing()
from root.solver import *
```

Draw the phase portrait for the following system of ode
$$
    \vec{\mathbf{x'}} = \begin{bmatrix}
        -\frac{1}{2} & 1 \\
        -1 & -\frac{1}{2} \\
    \end{bmatrix} \vec{\mathbf{x}}
$$


```python
%matplotlib inline
phase_portrait(
    [
        [-1/2, 1],
        [-1, -1/2]
    ],
    -5, 5, -5, 5, 15, "vector field"
)
```

Draw the phase portrait for the following system of ode
$$
    \vec{\mathbf{x'}} = \begin{bmatrix}
        -3 & \sqrt{2} \\
        \sqrt{2} & -2 \\
    \end{bmatrix} \vec{\mathbf{x}}
$$


```python
phase_portrait(
    [
        [-3, 1.414],
        [1.414, -2]
    ],
    -10, 10, -10, 10, 15, "stream"
)
```


```python

```

17a102e3d305da6ed806c2e222daa537c6e54701
ipynb
Jupyter Notebook
notebooks/system-of-ode-phase-portrait.ipynb
kaiyingshan/ode-solver
30c6798efe9c35a088b2c6043493470701641042
MIT
2019-02-17T23:15:20.000Z
2019-02-17T23:15:27.000Z
notebooks/system-of-ode-phase-portrait.ipynb
kaiyingshan/ode-solver
30c6798efe9c35a088b2c6043493470701641042
MIT
notebooks/system-of-ode-phase-portrait.ipynb
kaiyingshan/ode-solver
30c6798efe9c35a088b2c6043493470701641042
MIT
Qwen/Qwen-72B
1. YES
2. YES