Question

Given the differential equation, y′ =2x−y. Using Euler's method with step size of h=0.05, find y₂ if y(0)=2.

Answer 1

To find y₂ using Euler's method with a step size of h = 0.05 and the initial condition y(0) = 2, you can perform a series of calculations using the given formula. Calculate the next value of y by substituting the previous values of x and y into the formula. Repeat this process to find y₂.

Step-by-step explanation:

Euler's method is used to approximate the solution of a differential equation. To find y₂, we can start with the initial condition y(0) = 2 and use the given step size h = 0.05 to calculate the values of y at each step.

1. Set x₀ = 0 and y₀ = 2 as the initial values.
2. Calculate the next value of y using the formula y₁ = y₀ + h * (2x₀ − y₀).
3. Repeat step 2 to find y₂, substituting the values of x₀ = 0, y₀ = 2, and h = 0.05 into the formula.

By following these steps, you can find the value of y₂.