Mathematic Methods HW Solutions 55

Mathematic Methods HW Solutions 55 - (2 l + 1) P l , where...

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Chapter 12 1.1 y = a 1 xe x 1.2 y = a 0 e x 3 1.3 y = a 1 x 1.4 y = a 0 cos2 x + a 1 sin 2 x 1.5 y = a 0 cosh x + a 1 sinh x 1.6 y = ( A + Bx ) e x 1.7 y = Ax + Bx 3 1.8 y = a 0 (1 + x ) + a 2 x 2 1.9 y = a 0 (1 - x 2 ) + a 1 x 1.10 y = ( A + Bx ) e x 2 2.1 See Problem 5 . 3 2.4 Q 0 = 1 2 ln 1 + x 1 - x , Q 1 = x 2 ln 1 + x 1 - x - 1 3.2 xe x + 10 e x 3.3 (30 - x 2 ) sin x + 12 x cos x 3.4 - x sin x + 25 cos x 3.5 ( x 2 - 200 x + 9900) e - x 4.3 See Problem 5 . 3 5.1 See Problem 5 . 3 5.3 P 0 ( x ) = 1 P 1 ( x ) = x P 2 ( x ) = (3 x 2 - 1) / 2 P 3 ( x ) = (5 x 3 - 3 x ) / 2 P 4 ( x ) = (35 x 4 - 30 x 2 + 3) / 8 P 5 ( x ) = (63 x 5 - 70 x 3 + 15 x ) / 8 P 6 ( x ) = (231 x 6 - 315 x 4 + 105 x 2 - 5) / 16 5.8 5 P 0 - 2 P 1 5.9 2 P 2 + P 1 5.10 8 35 P 4 + 4 7 P 2 + 1 5 P 0 5.11 2 5 ( P 1 - P 3 ) 5.12 8 5 P 4 + 4 P 2 - 3 P 1 + 12 5 P 0 5.13 8 63 P 5 + 4 9 P 3 + 3 7 P 1 8.1 N = r π/ 2, r 2 cos nx 8.2 N = r 2 / 5, r 5 / 2 P 2 ( x ) 8.3 N = 2 1 / 2 , 2 - 1 / 2 xe - x/ 2 8.4 N = π 1 / 4 , π - 1 / 4 e - x 2 / 2 8.5 N = 1 2 π 1 / 4 , 2 π - 1 / 4 xe - x 2 / 2 9.1 3 2 P 1 - 7 8 P 3 + 11 16 P 5 ··· 9.2 1 4 P 0 + 1 2 P 1 + 5 16 P 2 - 3 32 P 4 ··· 9.3 5 P 2 + P 0 9.4 π 8 (3 P 1 + 7 16 P 3 + 11 64 P 5 ··· ) 9.5 1 2 P 0 - 5 8 P 2 + 3 16 P 4 ··· 9.6 P 0 + 3 8 P 1 - 20 9 P 2 ··· 9.7 1 3 P 0 + 2 5 P 1 - 11 42 P 2 ··· 9.8 1 2 (1 - a ) P 0 + 3 4 (1 - a 2 ) P 1 + 5 4 a (1 - a 2 ) P 2 + 7 16 (1 - a 2 )(5 a 2 - 1) P 3 ··· 9.9 P p n =
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Unformatted text preview: (2 l + 1) P l , where the sum is over odd l from 1 to n-1 when n is even, and over even l from 0 to n-1, when n is odd. 9.10 2 P 2 + P 1 9.11 8 5 P 4 + 4 P 2-3 P 1 + 12 5 P 9.12 2 5 ( P 1-P 3 ) 9.13 1 5 P + 4 7 P 2 = 3 35 (10 x 2-1) 9.14 1 2 P + 5 8 P 2 = 3 16 (5 x 2 + 1) 9.15-15 2 P 2 =-15 2 2 (3 x 2-1) 55...
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