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In Exercises 1-13 find all (xo. yo) for which Theorem 2.3.1 implies that the initial value problem y f(x, y). y(x) = yo has (a) a solution (b) a unique solution on some open interval that contains xo x² + y² sin x 3. y'=tan.xy Section 2.3 Existence and Uniqueness of Solutions of Nonlinear Equations 61 5. y'=(x² + y²)y¹/3 7. y'In(1+x² + y²) 9. y'=(x² + y²)1/2 11. y'=(x² + y²)² tan y 13. y'= 2. In xy 6. y' = 2xy 8. y'= 2x + 3y 10. y'=x(y2-1)2/3 12. y' = (x + y)¹/2

In Exercises 1-13 find all (xo. yo) for which Theorem 2.3.1 implies that the initial value problem y f(x, y). y(x) = yo has (a) a solution (b) a unique solution on some open interval that contains xo x² + y² sin x 3. y'=tan.xy Section 2.3 Existence and Uniqueness of Solutions of Nonlinear Equations 61 5. y'=(x² + y²)y¹/3 7. y'In(1+x² + y²) 9. y'=(x² + y²)1/2 11. y'=(x² + y²)² tan y 13. y'= 2. In xy 6. y' = 2xy 8. y'= 2x + 3y 10. y'=x(y2-1)2/3 12. y' = (x + y)¹/2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4 , 8 , 13 ONLY

In Exercises 1-13 find all (xo. yo) for which Theorem 2.3.1 implies that the initial value problem y'= f(x, y), y(x) = yo has (a) a solution (b) a unique solution on some open interval that contains. xo. 1. y'a 3. sin x y'=tan.xy Section 2.3 Existence and Uniqueness of Solutions of Nonlinear Equations 61 5. y' = (x² + y²)y¹/3 2. y' 4. y In xy 6. y' = 2xy 2x + 3y x - 4y 10. y'=x(y2-1)2/3 12. y' = (x + y)¹/2 8. y'= 7. y'In(1 + x² + y²) 9. y'=(x² + y2)1/2 11. y (x² + y²)² tan y 13. y'= x-1 14. Apply Theorem 2.3.1 to the initial value problem naft
Transcribed Image Text:In Exercises 1-13 find all (xo. yo) for which Theorem 2.3.1 implies that the initial value problem y'= f(x, y), y(x) = yo has (a) a solution (b) a unique solution on some open interval that contains. xo. 1. y'a 3. sin x y'=tan.xy Section 2.3 Existence and Uniqueness of Solutions of Nonlinear Equations 61 5. y' = (x² + y²)y¹/3 2. y' 4. y In xy 6. y' = 2xy 2x + 3y x - 4y 10. y'=x(y2-1)2/3 12. y' = (x + y)¹/2 8. y'= 7. y'In(1 + x² + y²) 9. y'=(x² + y2)1/2 11. y (x² + y²)² tan y 13. y'= x-1 14. Apply Theorem 2.3.1 to the initial value problem naft
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