By A. R. Forsyth

Vintage 19th-century paintings one of the best remedies of the subject. Differential equations of the 1st order, normal linear equations with consistent coefficients, integration in sequence, hypergeometric sequence, resolution via sure integrals, many different themes. Over 800 examples. Index.

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**Additional info for A Treatise on Differential Equations **

**Sample text**

42. 45. (2a2b- 3)- 3 x3 + n x" 48. v;ry 43. 2(a2 - 1 )0 46 . VsO 49. �32x8y6 44. 3 ��6r 41 2 47. V'ii Yx 50.

Xy 53. ( -�x3y-4r J 54. 2b-4 57. (a2a-3c58. 3r {a + b)b}- 21 62. 61 . (a -n n 65. (�) = (�) 1 2 . -3r3r3 1 6. -(2x2)S 20. (3;:r 24. [(3b + 1 )5 ]5 28. � (y4)6 32. (xy)o 36. x- s (2a) -6 (x-2)4 48. - 1 0 x l x •2 7 ( - 2rc-2)n (x2)3(y2)4(x3)7 {-2ab2b)4 (-3a 2)3 3 ( -�a2b3c2) (-3) -3 -x- s 4y5y-2 [ (x + y) - 2]2 (x4y -2) (x-2-2)2J (3y ) ix- 3y2 x- ly- 3 (a- 1 + b- 1 ) - 1 I Show that [ill]- 68. 6s5-2· r Consider a square whose area is length a. 462 Ifill. 69. 46- 1 rl square centimeters, and whose sides are of a2 = 25 so that a is a number whose square is 25.

Vs 2Yl) (Vz + 2Vs) 74. (Vh + 3) (Vh - 3) 73. (v3x + v'2J) (v3x - 2v'2J) In Exercises 75-86 rationalize the denominator. 77. v'3-2- 4 76. v'7-3- 9 75. v'2 + 3 78. Vx3- 5 80. 2 - 4v'2Y 79. 3Va-3+ l 81. 5 +-3VsY 82. v'3v'3- 5 In Exercises * * * - - 64 . - 3 52 THE FOUNDATIONS OF ALGEBRA 83. 111 v'2 + 1 � v2 - 1 Exercises 87. 89. Vx + Vs + V3 v'5 - V3 values for x and 84. 8 COMPLEX NUMBERS I)(- I ) = 86. vh Vy 2Va + and a po itive integer value for n to demonstrate the result . 88. 90. Find the step in the following " proof " that is incor rect.