 $$\left\{ \begin{array}{lcc}
            \dot{x}_{1}=-x_{1}^3 + u\\
             \\ \dot{x}_{2}=x_{1}
             \end{array}
\right.$$
 


```python
import sympy as sym
```


```python
#Con esto las salidas van a ser en LaTeX
sym.init_printing(use_latex=True)
```


```python
x_1, x_2 ,theta = sym.symbols('x_1 x_2 theta')
```


```python
X = sym.Matrix([x_1, x_2])
X
```


```python
f_1 = -x_1**3 - x_2
```


```python
f_2 = x_1
```


```python
F = sym.Matrix([f_1,f_2])
F
```


```python
# puntos de equilibrio del sistema
pes = sym.solve([f_1,f_2])
pes
```


```python
A = F.jacobian(X)
A
```


```python
A_1 = A.subs({x_1:0,x_2:0})
A_1
```


```python
A_1.eigenvals()
```


```python

```

b5a51aa727b63c143edac567f5e5a8027d6297ce
ipynb
Jupyter Notebook
parcial1_Noblia_ej3.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
parcial1_Noblia_ej3.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
parcial1_Noblia_ej3.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
Qwen/Qwen-72B
1. YES
2. YES