Weird Equation

Use implicit differentiation to get the slope of the function:

$\large{e^y + yx - 2y - x^2 + 8 = 0 \\ e^y \frac{dy}{dx} + y + x \frac{dy}{dx} - 2 \frac{dy}{dx} - 2x = 0 \\ \frac{dy}{dx} (e^y + x - 2) = 2x - y \\ \frac{dy}{dx} = \frac{2x - y}{e^y + x - 2} }$

Write a computer program to start at $(3,0)$ and step backward until $x = 2.98$ . Integrate the slope to update the $y$ value. When the program terminates, $y \approx -0.06$ .

import math

x = 3.0
y = 0.0

dx = 10.0**(-6.0)

while x >= 2.98:

    num = 2.0*x - y
    denom = math.exp(y) + x - 2.0

    yp = num / denom

    y = y + yp * (-dx)

    x = x - dx

print y


#### Result is -0.0613348355773