Use Theorem 5.4 to show that each of the following initial-value problems has a unique solution, and find the solution.
a. y' = y cos t, 0≤ t ≤ 1, y(0) = 1.
b. y' = 2/t y + t2et, 1≤ t ≤ 2, y(1) = 0.
c. y' = −2/t y + t2et, 1≤ t ≤ 2, y(1) =√2e.
d. y' = (4t3y)/(1 + t4), 0≤ t ≤ 1, y(0) = 1.