Question 4

(sec ) tan 0 2 dy x y x xdx π + = ≤ <    5. 2cos tandyx y xdx + = 0 2x π ≤ <   6. 22 logdyx y x xdx + = 7. 2log logdyx x y xdx x+ = 8. (1 + x2) dy + 2xy dx = cot x dx (x ≠ 0) 9. cot 0 ( 0)dyx y x xy x xdx + − + = ≠ 10. ( ) 1 dyx y dx+ = 11. y dx + ( x - y2) dy = 0 12. 2( 3 ) ( 0) dyx y y y dx+ = > . For each of the differential equations given in Exercises 13 to 15, find a particular solution satisfying the given condition: 13. 2 tan sin ; 0 when 3 dy y x x y xdx π+ = = = 14. 2/2 1(1 ) 2 ; 0 when 1 dyx xy y xdx x + + = = = + 15. 3 cot sin 2 ; 2 when 2 dy y x x y xdx π− = = = 16. Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point. 17. Find the equation of a curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5. 18. The Integrating Factor of the differential equation 22dyx y xdx − = is (A) e-x (B) e- y (C) 1 x (D) x 19. The Integrating Factor of the differential equation 2(1 ) dxy yx dy − + = ( 1 1)− < <ay y is (A) 2 / 1y − (B) 2 / 1y − (C) 2 / 1 y− (D) 2 1 y−