Use Euler's method to calculate the first three approximations to the given initial value problem for the specified increment size. Round your results to four decimal places.
-y = -x(1 - y), y(2) = 3, dx = 0.2
A) y1 = 3.8000, y2 = 5.0320, y3 = 6.9674
B) y1 = 7.0000, y2 = 50.3200, y3 = 69.6736
C) y1 = 0.7000, y2 = 2.5160, y3 = 3.4837
D) y1 = 2.8000, y2 = 10.0640, y3 = 13.9347

Question

Quizplus · Accepted Answer

Euler's method involves using the formula y_(n+1) = y_n + f(x_n, y_n) * dx to iteratively calculate the next value based on the current value and the slope at the current point. Given y' = -x(1 - y), y(2) = 3, and dx = 0.2, we calculate the first three approximations as follows: y1 = 3 + (-2(1-3))*0.2 = 3.8, y2 = 3.8 + (-2.2(1-3.8))*0.2 = 5.032, y3 = 5.032 + (-2.4(1-5.032))*0.2 = 6.9674.

Use Euler's Method to Calculate the First Three Approximations to the Given