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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 1

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 1

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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1 please Why we get x^2+3x+y^2-2y=c
6:51 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 4. dx bx + cy dy axby dx bx-cy 5. 74 x > 0 <=0 X 1 Sience 6. (yety cos(2x) -2exy sin(2x)+2x)+(xexy cos(2x)-3) y' = 0 7. (y/x+6x) + (lnx - 2) y' = 0, y dy 8. + (x² + y2)3/2 (x² + y2) 3/2 dx 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 giver equation is exact, and then solve it using that value of b. S 11. (xy² + bx²y) + (x+y)x²y = 0 12. (ye2xy + x) + bxe²xyy' = 0 13. Assume that equation (6) meets the requirements of Theore 2.6.1 in a rectangle R and is therefore exact. Show that a possib function(x, y) is
Transcribed Image Text:6:51 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 4. dx bx + cy dy axby dx bx-cy 5. 74 x > 0 <=0 X 1 Sience 6. (yety cos(2x) -2exy sin(2x)+2x)+(xexy cos(2x)-3) y' = 0 7. (y/x+6x) + (lnx - 2) y' = 0, y dy 8. + (x² + y2)3/2 (x² + y2) 3/2 dx 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 giver equation is exact, and then solve it using that value of b. S 11. (xy² + bx²y) + (x+y)x²y = 0 12. (ye2xy + x) + bxe²xyy' = 0 13. Assume that equation (6) meets the requirements of Theore 2.6.1 in a rectangle R and is therefore exact. Show that a possib function(x, y) is
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