Question 1

Given the IVP

y⁽¹⁾(t) = 1 - 0.25 y(t) + 0.2 t
y(0) = 1

approximate y(1) using four steps of Euler's method, Heun's method, and 4th-order Runge Kutta.

Answer: 1.754495239, 1.755786729, 1.755760161

Question 2

Given the same ODE as in Question 1, but with the initial condition y(1) = 2, approximate y(2.0).

Answer: 2.708990479, 2.711573457, 2.711520324