<jupyter_start><jupyter_text>$$\left\{ \begin{array}{lcc}            \dot{x}_{1}=2x_{2}+x_{1}(x_{1}^{2}+2x_{2}^{4}) \\             \\ \dot{x}_{2}=-2x_{1}+x_{2}(x_{1}^{2}+x_{2}^{4})             \end{array}\right.$$<jupyter_code>import sympy as sym
#Con esto las salidas van a ser en LaTeX
sym.init_printing(use_latex=True)
x_1, x_2 ,theta = sym.symbols('x_1 x_2 theta')
X = sym.Matrix([x_1, x_2])
X
f_1 = 2*x_2 + x_1*(x_1**2 + 2*x_2**4)
f_1
f_2 = -2*x_1 + x_2*(x_1**2 + x_2**4)
f_2
F = sym.Matrix([f_1,f_2])
F
# puntos de equilibrio del sistema
pes = sym.solve([f_1,f_2])
pes
A = F.jacobian(X)
A
sym.latex(A)
A_1 = A.subs({x_1:0,x_2:0})
A_1
A_1.eigenvals()
expr = 2*x_1 *F[0] + 2*x_2*F[1]
expr = expr.simplify()
sym.latex(expr)
expr<jupyter_output><empty_output>
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