Using the improved Euler's method, approximate the solution to the predator prey problem in Example 2. Compare the new solution to that obtained by Euler's method using Δt = 0.1 over the interval 0 ≤t ≤ 3. Graph the solution trajectories for both solutions.

Data from example 2

Use Euler's method to find the trajectory through the point (1, 2) in the phase plane for the predator prey model in Example 1.