C. sin * dx (4 points possible) V1- X 12. Find the exact solutions to the following differential equations. a. y'= ) 3-X xy ", x > 0, y(1) = 2 (6 points possible) b. y' = y. y(2) = 3 (5 points possible) C. dx dy + xy= x, y(0) = = (6 points possible) 13. The slope field for = = _ is shown in dx the figure to the right. a. Sketch solution curves with initial conditions: (6 points possible) i. (0, 1) i. (1, 0) All 121 131 14 III. (0, 3) Does lim y exist? If so, what is its value? (4 points possible)C. Find a possible solution to the differential equation. (5 points possible) 14. The region bounded by y = 0 and y = kx - x is revolved around the y-axis to form a solid whose volume is 10. What are the exact possible values of ? (8 points possible) Hint: Use cylindrical shells. 15. Find the volume of the solid obtained by rotating the region bounded by xy = 4 and y= (x -3) about the x-axis. (8 points possible) 16. Any cross-section of a particular solid cut by a plane perpendicular to the x-axis is a square whose diagonal lies on the parabolas y'= 4x and x = 4y. Find the volume of the solid. (8 points possible) 17. A rumor is spreading through town at a rate of ( + 10t new people/day. Approximately how many people hear the rumor during the second week after it is first heard? (9 points possible)