Page 58 - Schaum's Outline of Differential Equations
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CHAP. 5] EXACT FIRST-ORDER DIFFERENTIAL EQUATIONS 41
In Problems 5.41 through 5.55, find an appropriate integrating factor for each differential equation and solve.
5.41. (y+ 1) dx-xdy = 0 5.42. y dx+(l-x)dy = 0
2
2
3 3
5.43. (x + y + y ) dx-xdy = 0 5.44. (y + x y ) dx + xdy = 0
2
4 2
2
5.45. (y + x y ) dx + xdy = 0 5.46. (3x y -x )dx + dy = 0
2
5.47. dx-2xydy = 0 5.48. 2xy dx + y dy = 0
5.49. ydx + 3xdy = 0
2
2
2
2 2
5.51. xy 2 dx+(x y + x y) dy = 0 5.52. ^y dx + x ydy = 0
3
2 4
2
3
5.53. (y + x + xy ) dx-xdy = 0 5.54. O / - y) dx + (x y - x) dy = 0
2 2
4
5.55. 3x y dx + (2x*y + x^y ) dy = 0
In Problems 5.56 through 5.65, solve the initial-value problems.
5.56. Problem 5.10 with x(0) = 2 5.57. Problem 5.10 with x(2) = 0
y
5.58. Problem 5.10 with *(!) = -5 5.59. Problem 5.24 with (l) = - 5
5.60. Problem 5.26 with y(0) = -1 5.61. Problem 5.31 with y(0) = -2
5.62. Problem 5.31 with y(2) = -2 5.63. Problem 5.32 with y(2) = -2
5.64. Problem 5.36 with XI) = 5 5.65. Problem 5.38 with x(\) = -2
