Question

Let y(t) be the solution to y′=8te⁻ʸ satisfying y(0)=3.

Use Euler's Method with time step h=0.2 to approximate y(0.2), y(0.4), y(0.6), y(0.8), y(1.0)

Answer 1

Euler's Method with a time step of h=0.2 can be used to approximate the solution to the given differential equation. The values of y at different time points, y(0.2), y(0.4), y(0.6), y(0.8), and y(1.0), can be found using the iterative formula y[i+1] = y[i] + h * (8 * t[i] * e^(-y[i]))

Step-by-step explanation:

Euler's Method is a numerical method used to approximate the solution to a first-order differential equation. To use Euler's Method, we start with the initial condition y(0) = 3 and use the given differential equation y' = 8te^(-y) to find the values of y at different time points. With a time step of h = 0.2, we can approximate y(0.2), y(0.4), y(0.6), y(0.8), and y(1.0) using the iterative formula:

y[i+1] = y[i] + h * (8 * t[i] * e^(-y[i]))

where t[i] = i * h and y[i] represents the approximate value of y at time t[i].