Consider the initial-value problem dy/dt = y2 − 2y + 1, y(0) = 2. (a) Using Euler’s...

Consider the initial-value problem dy/dt = y2 − 2y + 1, y(0) = 2.

(a) Using Euler’s method with = 0.5, graph an approximate solution over the interval 0 ≤ t ≤ 2.

(b) What happens when you try to repeat part (a) with = 0.05?

(c) Solve this initial-value problem by separating variables, and use the result to explain your observations in parts (a) and (b).