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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 |
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