For the following initial-value problems, show that the given equation implicitly defines a solution. Approximate y(2) using

Question:

For the following initial-value problems, show that the given equation implicitly defines a solution. Approximate y(2) using Newton's method.
a. y' = − y3 + y/((3y2 + 1)t) , 1≤ t ≤ 2, y(1) = 1; y3t + yt = 2
b. y' = − (y cos t + 2tey)/(sin t + t2ey + 2) , 1≤ t ≤ 2, y(1) = 0; y sin t + t2ey + 2y = 1