Chapter 5.3, Problem 7ES

Repeat Exercise 5 using Taylor’s method of order four.

5. Use Taylor’s method of order two to approximate the solutions for each of the following initial-value problems.

1. a. y′ = y/t − (y/t)², 1 ≤ t ≤ 1.2, y(1) = 1, with h = 0.1
2. b. y′ = sin t + e^−t, 0 ≤ t ≤ 1, y(0) = 0, with h = 0.5
3. c. y′ = (y² + y)/t, 1 ≤ t ≤ 3, y(1) = −2, with h = 0.5
4. d. y′ = −ty + 4ty⁻¹, 0 ≤ t ≤ 1, y(0) = 1, with h = 0.25