Question

Consider the differential equation dy/dx = -x - y.

1. Use Euler's method with Δx = 0.1 to estimate y when x = 1.4 for the solution curve satisfying y(1) = 1.
y(1.4)

Answer 1

To estimate the value of y when x = 1.4 using Euler's method with Δx = 0.1, we can follow the steps provided.

Step-by-step explanation:

To estimate the value of y when x = 1.4 using Euler's method with Δx = 0.1, we can use the following steps:

1. Start with the initial condition y(1) = 1.
2. Calculate the slope at x = 1 and y = 1 using the given differential equation dy/dx = -x - y. The slope is -1 - 1 = -2.
3. Using the slope, calculate the increment in y: Δy = (-2)(0.1) = -0.2.
4. Add the increment to the previous value of y: y(1.1) = 1 + (-0.2) = 0.8.
5. Repeat steps 2-4 until x = 1.4. Each time, update the value of x by adding Δx = 0.1 and calculate the new value of y by adding the increment Δy = -2Δx to the previous value of y.
6. When x = 1.4, y ≈ 0.564.