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(a) Check whether the IVP x y' y (0) = 4. y-4' satisfies the hypotheses of the Picard-Lindelöf theorem. (b) Find all the solutions of the IVP defined in (a). Is this result in contradiction with the result obtained in (a)? Explain your answer. (c) Determine the smallest b>0 such that the BVP I 2y" — 18y = tanh(x), y(0) = 0, y' (b) = 3, does not have a unique solution.

(a) Check whether the IVP x y' y (0) = 4. y-4' satisfies the hypotheses of the Picard-Lindelöf theorem. (b) Find all the solutions of the IVP defined in (a). Is this result in contradiction with the result obtained in (a)? Explain your answer. (c) Determine the smallest b>0 such that the BVP I 2y" — 18y = tanh(x), y(0) = 0, y' (b) = 3, does not have a unique solution.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 40E
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(a) Check whether the IVP X y' y(0) = 4. Y-4 satisfies the hypotheses of the Picard-Lindelöf theorem. (b) Find all the solutions of the IVP defined in (a). Is this result in contradiction with the result obtained in (a)? Explain your answer. (c) Determine the smallest b>0 such that the BVP I 2y" - 18y = tanh(x), y(0) = 0, y' (b) = 3, does not have a unique solution.
Transcribed Image Text:(a) Check whether the IVP X y' y(0) = 4. Y-4 satisfies the hypotheses of the Picard-Lindelöf theorem. (b) Find all the solutions of the IVP defined in (a). Is this result in contradiction with the result obtained in (a)? Explain your answer. (c) Determine the smallest b>0 such that the BVP I 2y" - 18y = tanh(x), y(0) = 0, y' (b) = 3, does not have a unique solution.
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