Question

Let y = f(x) be the solution to the differential equation dy/dx = x - y - 1 with the initial condition f(1) = -2. What is the approximation for f(1.4) if Euler's method is used, starting at r = 1 with two steps of equal size?

A) -2
B) -1.24
C) -1.22
D) -0.64
E) 0.2

Answer 1

To approximate f(1.4) using Euler's method, calculate two steps of equal size starting at x=1 and using the given differential equation and initial condition.

Step-by-step explanation:

To approximate the value of f(1.4) using Euler's method, we need to take two steps of equal size starting at x=1. Given the differential equation dy/dx = x - y - 1 and the initial condition f(1) = -2, we can use Euler's method to iteratively calculate the values of y at each step.

Step 1: Calculate the first step using the equation y1 = y0 + h(f'(x0, y0)) where h is the step size and f'(x0, y0) is the derivative of f(x) at the initial point (x0, y0).

Step 2: Use the calculated value of y1 as the new initial point and repeat the calculation to find y2 = y1 + h(f'(x1, y1)).

After two steps, we will have an approximate value for f(1.4).