Determine the largest possible interval of validity of the solution for the IVP
cos x
dy/dx
= y sin x −
√
x − 1, y(
3/2
) = 0.
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Answer:
According to the Existence and Uniqueness Theorem, therefore, a continuous and differentiable solution of this initial value problem is guaranteed to exist uniquely on any interval containing t0 = 2π but not containing any of the discontinuities. The largest such intervals is (3π/2, 5π/2).
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