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In each of Problems 9 and 10, solve the given initial value problem and determine at least approximately where the solution is valid. 9. (2x - y) + (2y - x) y' = 0, y(1) = 3 has In

In each of Problems 9 and 10, solve the given initial value problem and determine at least approximately where the solution is valid. 9. (2x - y) + (2y - x) y' = 0, y(1) = 3 has In

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Problems Determine whether each of the equations in Problems 1 through 8 is exact. If it is exact, find the solution. 1. (2x + 3) + (2y - 2) y' = 0 2. (2x+4y) + (2x - 2y) y' = 0 3. (3x² - 2xy + 2) + (6y² - x² + 3) y' = 0 dy ax + by dx bx + cy ax- - by bx - cy 4. dy dx 5. 6. (yexy cos(2x)-2exy sin(2x)+2x)+(xexy cos(2x) - 3) y' = 0 7. (y/x+6x) + (lnx - 2) y' = 0, x > 0 y dy + 2 (x² + y2)3/2 (x² + y²) 3/2 dx x 8. In each of Problems 9 and 10, solve the given initial value problem and determine at least approximately where the solution is valid. 9. (2x - y) + (2y - x) y' = 0, y(1) = 3 10. (9x² + y − 1) - (4y - x) y' = 0, y(1) = 0 In each of Problems 11 and 12, find the value of b for which the given equation is exact, and then solve it using that value of b. 11. (xy²+bx²y) + (x + y)x²y' = 0 12. (ye²xy + x) + bxe²xyy' = 0 (x, y) = = 0 xo 13. Assume that equation (6) meets the requirements of Theorem 2.6.1 in a rectangle R and is therefore exact. Show that a possible function(x, y) is where (xo, yo) is a point in R. INO Yo M(s, yo) ds + 14. Show is also exa In each of exact but factor. Th 15. x²y N(x, t) dt, 16. (x 17. SH only, the has an In eac the g 18. 19. 20. 21. 22 us C in
Transcribed Image Text:Problems Determine whether each of the equations in Problems 1 through 8 is exact. If it is exact, find the solution. 1. (2x + 3) + (2y - 2) y' = 0 2. (2x+4y) + (2x - 2y) y' = 0 3. (3x² - 2xy + 2) + (6y² - x² + 3) y' = 0 dy ax + by dx bx + cy ax- - by bx - cy 4. dy dx 5. 6. (yexy cos(2x)-2exy sin(2x)+2x)+(xexy cos(2x) - 3) y' = 0 7. (y/x+6x) + (lnx - 2) y' = 0, x > 0 y dy + 2 (x² + y2)3/2 (x² + y²) 3/2 dx x 8. In each of Problems 9 and 10, solve the given initial value problem and determine at least approximately where the solution is valid. 9. (2x - y) + (2y - x) y' = 0, y(1) = 3 10. (9x² + y − 1) - (4y - x) y' = 0, y(1) = 0 In each of Problems 11 and 12, find the value of b for which the given equation is exact, and then solve it using that value of b. 11. (xy²+bx²y) + (x + y)x²y' = 0 12. (ye²xy + x) + bxe²xyy' = 0 (x, y) = = 0 xo 13. Assume that equation (6) meets the requirements of Theorem 2.6.1 in a rectangle R and is therefore exact. Show that a possible function(x, y) is where (xo, yo) is a point in R. INO Yo M(s, yo) ds + 14. Show is also exa In each of exact but factor. Th 15. x²y N(x, t) dt, 16. (x 17. SH only, the has an In eac the g 18. 19. 20. 21. 22 us C in
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