This script will allow you to generate a slope field for a given dy/dx on the x and y axes [-3, 3].

When inputting your dy/dx you must explicitly define every operation

Examples of inputting different slopes are below:

if dy/dx = 2x/y then input 2*x/y

if dy/dx = 0.5x+y then input 0.5*x+y

Watch a tutorial at https://www.youtube.com/watch?v=bT391K229Bs

from matplotlib.pyplot import *
from math import *

# The x-axis minimum is set to -3, change this value to change the window
x_axis_min = -3

# Automatically set the x&y axes based on the x-min 
y_axis_min = x_axis_min
x_axis_max = abs(x_axis_min)
y_axis_max = abs(x_axis_min)
# create a list of x and corresponding y lattice point coordinates using axes max/min
x = list(range(x_axis_min, x_axis_max + 1, 1))  # range(start, stop, step)
y = list(range(x_axis_min, x_axis_max + 1, 1))  # range(start, stop, step)

# allowed math functions for eval
allowed_math = {
    "sqrt": sqrt, "sin": sin, "cos": cos, "tan": tan,
    "log": log, "exp": exp, "pi": pi, "e": e,
    "asin": asin, "acos": acos, "atan": atan,
    "abs": abs, "pow": pow
}

print("Input your dy/dx")
print("-Explicitly define every")
print("operation")
print("Ex: 2x/y input as 2*x/y")

# Ask user for the dydx function
dydx_expression = input("dy/dx= ")

def dydx(_x, _y):
    env = {"x": _x, "y": _y, "__builtins__": {}}
    env.update(allowed_math)
    try:
        return eval(dydx_expression, env)
    except Exception as e:
        print("Error in dydx function:", e)
        return 100

# create list of x, y pairs
x_y = []
xm = []
ym = []

# create nested list of lists of all ordered pairs then extract xm and ym lists
for i in range(len(x)):
    for j in range(len(y)):
        x_y.append((x[i], y[j]))

for i in range(len(x_y)):
    xm.append(x_y[i][0]) # select all x midpoint values

for i in range(len(x_y)):
    ym.append(x_y[i][1]) # select all y midpoint values   

# create x and y axes, extend by 1 in each direction so the slope lines are visible
axis((x_axis_min-1,x_axis_max+1,y_axis_min-1,y_axis_max+1))   # axis(Xmin,Xmax,Ymin,Ymax)
axis("on")                  # mathplotlib: turn axes "on"
grid(False)                 # mathplotlib: turn grid "off"

# mathplotlib: draw arrows(x,y,dx,dy) where (x,y) start and (x + dx, y + dy) is end
# i.e. arrows(xs=xm-dx, ys=ym-dy, 2dx, 2dy)
d  = 0.250 # initial value of half the length of each line segment
xs = []
ys = []
m  = []
dx = []
dy = []

for i in range(len(xm)):
    m.append(dydx(xm[i],ym[i]))  # call dydx to calculate m for each (xm,ym) ordered pair
for i in range(len(xm)):
    dx.append((d)/(sqrt(1 + pow(m[i],2)))) # calculate dx for each xs
for i in range(len(xm)):
    dy.append(m[i] * dx[i])      # calculate dy for each xs
for i in range(len(xm)):
    xs.append(xm[i] - dx[i])     # xs = starting x values of arrows
    ys.append(ym[i] - dy[i])     # ys = starting y values of arrows

# draw arrows starting at each (xs,ys) ordered pair and moving by 2dx and 2dy
for i in range(len(xs)):
  arrow(xs[i],ys[i],2*dx[i],2*dy[i],color="red",head_width = 0.05)

show()  # mathplotlib show display

print("re-execute script to do")
print("another slopefield")