Use the Extrapolation Algorithm with TOL = 104 to approximate the solutions to the following initial-value problems:

Question:

Use the Extrapolation Algorithm with TOL = 10−4 to approximate the solutions to the following initial-value problems:
a. y' = (y/t)2 + y/t, 1≤ t ≤ 1.2, y(1) = 1, with hmax = 0.05 and hmin = 0.02.
b. y' = sin t + e−t, 0≤ t ≤ 1, y(0) = 0, with hmax = 0.25 and hmin = 0.02.
c. y' = (y2 + y)/t, 1≤ t ≤ 3, y(1) = −2, with hmax = 0.5 and hmin = 0.02.
d. y' = −ty + 4t/y, 0≤ t ≤ 1, y(0) = 1, with hmax = 0.25 and hmin = 0.02.