code: def runge_kutta4(y, x, dx, f):
      """computes 4th order Runge-Kutta for dy/dx.
  
      Parameters
      ----------
  
      y : scalar
          Initial/current value for y
      x : scalar
          Initial/current value for x
      dx : scalar
          difference in x (e.g. the time step)
      f : ufunc(y,x)
          Callable function (y, x) that you supply to compute dy/dx for
          the specified values.
  
      """
  
      k1 = dx * f(y, x)
      k2 = dx * f(y + 0.5 * k1, x + 0.5 * dx)
      k3 = dx * f(y + 0.5 * k2, x + 0.5 * dx)
      k4 = dx * f(y + k3, x + dx)
  
      return y + (k1 + 2 * k2 + 2 * k3 + k4) / 6.0
  
imports: from __future__ import print_function
  from collections import defaultdict, deque
  import copy
  import inspect
  import numpy
label_desc: Use image node_id 1 for calling a global function with example usage: runge_kutta4(y, x, dx, f) and returns: unknown