code: def _euler(red, x0, x1, y0, a):
      """
      Euler's method for numerical integration.
      From x0 to x1 with initial values given at x0 as vector y0.
      """
  
      A = sympify(x0)._to_mpmath(mp.prec)
      B = sympify(x1)._to_mpmath(mp.prec)
      y_0 = [sympify(i)._to_mpmath(mp.prec) for i in y0]
      h = B - A
      f_0 = y_0[1:]
      f_0_n = 0
  
      for i in range(a):
          f_0_n += (
              sympify(DMFsubs(red[i], A, mpm=True))._to_mpmath(mp.prec)
              * y_0[i]
          )
      f_0.append(f_0_n)
  
      sol = []
      for i in range(a):
          sol.append(y_0[i] + h * f_0[i])
  
      return sol
  
imports: from sympy.core.sympify import sympify
  from sympy.holonomic.holonomic import DMFsubs
  from mpmath import mp
label_desc: Use image node_id 2 for calling a global function with example usage: _euler(red, x0, x1, y0, a) and returns: sol