 $$\left\{ \begin{array}{lcc}
            \dot{x}_{1}=2x_{2}+x_{1}(x_{1}^{2}+2x_{2}^{4}) \\
             \\ \dot{x}_{2}=-2x_{1}+x_{2}(x_{1}^{2}+x_{2}^{4})
             \end{array}
\right.$$
 


```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 = 2*x_2 + x_1*(x_1**2 + 2*x_2**4)
f_1
```


```python
f_2 = -2*x_1 + x_2*(x_1**2 + x_2**4)
f_2
```


```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
sym.latex(A)
```




    '\\left[\\begin{matrix}3 x_{1}^{2} + 2 x_{2}^{4} & 8 x_{1} x_{2}^{3} + 2\\\\2 x_{1} x_{2} - 2 & x_{1}^{2} + 5 x_{2}^{4}\\end{matrix}\\right]'




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


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


```python
expr = 2*x_1 *F[0] + 2*x_2*F[1]
expr = expr.simplify()
```


```python
sym.latex(expr)
```




    '2 x_{1}^{4} + 4 x_{1}^{2} x_{2}^{4} + 2 x_{1}^{2} x_{2}^{2} + 2 x_{2}^{6}'




```python
expr
```


```python

```

cdb3852719af32fd27a0be94849fe0c9265cf42d
ipynb
Jupyter Notebook
parcial1_Noblia_ej2.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
parcial1_Noblia_ej2.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
parcial1_Noblia_ej2.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
Qwen/Qwen-72B
1. YES
2. YES