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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) 1/2919tti aur ¹/2

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) 1/2919tti aur ¹/2

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 34CR
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can usually be found only by solving the equation and examining the solution. It is the singularities will depend on the initial condition as well as on the differential e 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. (t-3) y' + (Int) y = 2t, y(1)=2 y' + (tant) y = sint, y(π) = 0 (4-t²) y' + 2ty = 3t², y(-3) = 1 2. 3. 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) ¹/2 6919ttid 2001 7. In |ty| 6. 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 on the initial value yo. 8. y' = 9. y' = -4t/y, 10. y' = 2ty², 11. y'+y³ = 0, 1² y(1+t³) 12. y' = 10.00 y(0) = yo y(0) = yo y(0) = yo In each of Probl sketch) several how solutions a depends on the G 13. y'= G 14. y' = G 15. y' = G 16. y' = Om 17. Consider Example 3 in t y(0) = yo abimis a. Is the nya noi find it. b. Is the find it. c. Cons problem. at t = 2. 18. a. Veri solutions Where a
Transcribed Image Text:can usually be found only by solving the equation and examining the solution. It is the singularities will depend on the initial condition as well as on the differential e 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. (t-3) y' + (Int) y = 2t, y(1)=2 y' + (tant) y = sint, y(π) = 0 (4-t²) y' + 2ty = 3t², y(-3) = 1 2. 3. 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) ¹/2 6919ttid 2001 7. In |ty| 6. 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 on the initial value yo. 8. y' = 9. y' = -4t/y, 10. y' = 2ty², 11. y'+y³ = 0, 1² y(1+t³) 12. y' = 10.00 y(0) = yo y(0) = yo y(0) = yo In each of Probl sketch) several how solutions a depends on the G 13. y'= G 14. y' = G 15. y' = G 16. y' = Om 17. Consider Example 3 in t y(0) = yo abimis a. Is the nya noi find it. b. Is the find it. c. Cons problem. at t = 2. 18. a. Veri solutions Where a
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