(Solution) - Use Algorithm 5 4 to approximate the solutions to the initial value -(2025 Original AI-Free Solution)

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Use Algorithm 5.4 to approximate the solutions to the initial-value problems in Exercise 3.
In Exercise 3
a. y' = y/t ? (y/t)2, 1? t ? 2, y(1) = 1, with h = 0.1; actual solution y(t) = t/(1 + ln t).
b. y' = 1+y/t+(y/t)2, 1? t ? 3, y(1) = 0, with h = 0.2; actual solution y(t) = t tan(ln t).
c. y' = ?(y + 1)(y + 3), 0 ? t ? 2, y(0) = ?2, with h = 0.1; actual solution y(t) = ?3 + 2/(1 + e?2t).
d. y' = ?5y+5t2+2t, 0? t ? 1, y(0) = 1/3, with h = 0.1; actual solution y(t) = t2+1/3 e?5t .