Exercise 1. Solve the logistic differential equation with a time varying carrying capacity and the initial condition .
Exercise 2. Solve with initial condition , and find the values of .
Exercise 3. Develop Euclid's Method. Use it to approximate the solution to at . Show the results graphically in comparison with the actual solution.
Exercise 4. Approximate for the initial value problem using Euclid's method with and compare with the actual value.
Exercise 5. Approximate for the initial value problem using the improved Euclid's method with and compare with the actual value.
Exercise 6. Approximate for the initial value problem using the fourth-order Runge-Kutta method with and compare with the actual value.