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Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Problems In each of Problems 1 through 4, determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist. 1. (1-3) y' + (Int) y = 21, y(1) = 2 2. y' + (tant) y = sint, y(π) = 0 3. (4-1²) y' + 2ty = 3t², y(-3) = 1 4. (Int) y' + y = cott, y(2) = 3 In each of Problems 5 through 8, state where in the ty-plane the hypotheses of Theorem 2.4.2 are satisfied. 5. y' = (1-₁² - y²) ¹1/216171810 6. 7. 8. y' = 9. y' = -4t/y, 10. y' = 2ty², 11. y' + y² = 0, 1² y(1+1³) In |ty| y' y² = ₁-1² + y² y' = (1² + y²) 3/2 1+1² 3y - y² In each of Problems 9 through 12, solve the given initial value problem and determine how the interval in which the solution exists depends 18 on the initial value yo. 12. y' = y(0) = yo as we ell as on the dif y(0) = yo y(0) = yo y(0) = yo In ear sketc how depe G G G 17. Exa
Transcribed Image Text:Problems In each of Problems 1 through 4, determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist. 1. (1-3) y' + (Int) y = 21, y(1) = 2 2. y' + (tant) y = sint, y(π) = 0 3. (4-1²) y' + 2ty = 3t², y(-3) = 1 4. (Int) y' + y = cott, y(2) = 3 In each of Problems 5 through 8, state where in the ty-plane the hypotheses of Theorem 2.4.2 are satisfied. 5. y' = (1-₁² - y²) ¹1/216171810 6. 7. 8. y' = 9. y' = -4t/y, 10. y' = 2ty², 11. y' + y² = 0, 1² y(1+1³) In |ty| y' y² = ₁-1² + y² y' = (1² + y²) 3/2 1+1² 3y - y² In each of Problems 9 through 12, solve the given initial value problem and determine how the interval in which the solution exists depends 18 on the initial value yo. 12. y' = y(0) = yo as we ell as on the dif y(0) = yo y(0) = yo y(0) = yo In ear sketc how depe G G G 17. Exa
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