The following are not stiff differential equations, however, the techniques may still be applied.

Question 1

Given the IVP

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

approximate y(0.5), y(1), and y(1.5) using the backward-Euler's method.

Answer: 1.377777778, 1.76, 2.145454545.

Question 2

Given the same ODE as in Question 1, but with the initial condition y(1) = 2, approximate y(1.5) and y(2.0).

Answer: 2.355555556 and 2.72