A Treatise on Differential Equations by George Boole

By George Boole

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4 1 } . 69. 58 - J!. 2. 58 - 2. 4 1 x x - + - = c a ;to 0, b ;to 0, a ;to -b a b ' 71. ab (� i ) + = ab . c bx + ax = abc ( a + b ) x = abc ( a + b ) x abc -'-----"-- = -a+b a+b abc X = -a+b 36 © 2008 Pearson Education , Inc . , Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of thi s material may be reproduced, in any form or by any means , without permission in wri ting from the publisher. Section 1 . 1 : Linear Equations 7 3.

X2 _ .!. fi5 x = ±5 (x-�J The solution set is {-5, 5} . 31. CT ( . [25 x + 2 ±5 x = -2 ± 5 x = 3 or x = -7 The solution set is {- 7, 3} . 4x2 - 8x + 3x - 9 = -3 4x2 - 5x - 6 0 (4x + 3) (x - 2) = O 4x + 3 = O or x - 2 = O 3 x=2 x = - - or 4 29. ' = + 4 (x _ l) 2 = 4 .!. 1 1 X = -±4 2 X = -3 or x = --I 4 4 x - I = ± J4 x - I = ±2 x - I = 2 or x - l = -2 x 3 or x = - 1 The solution set is { -I, 3} . The solution set is = {-�,%}. 40 © 2008 Pearson Education , inc . , Upper Saddle River, NJ. All rights reserved.

Chapter R: Review 77. 79. 2x ( x2 + 1 )1/2 + x2 2"1 ( x 2 + 1 )-1/2 . 2x = 2x ( X2 + 1 )112 + ( 2 x3 1/2 X + 1) 2x ( x2 + 1 )112 . ( x2 + 1 )1/2 + x3 ( X 2 + 1 )1/2 2x ( x2 + l )1/2+1/2 + x3 2x ( x 2 + 1 Y + x3 ( X 2 + 1 )1/2 ( X 2 + 1 )112 2x 3 + 2x + x3 3x3 + 2x ( X2 + 1 )1/2 (X 2 + 1 )1/2 X ( 3 X2 + 2 ) ( X2 + 1 )112 83 . -- �4x + 3 · ,x > 5 � + �x - 5 . = 2�x - 5 5 �4x + 3 J4;+3 · 5 · J4;+3 + � · 2 · � 10�x - 5 �4x + 3 3 5 - 1 ( 4x x+ -)5+ 24x( x+- 5 ) O�( ) ( 3 ) 20x + 15 + 2x -10 10�( x - 5 )( 4x + 3 ) 22x + 5 10�( x - 5 )( 4x + 3 ) = 85.

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