计算机数学基础(第三版)习题参考答案第6-8章
计算机数学基础(第三版)习题参
考答案第6-8章
习题6.1
1.(1) D; (2) A; (3) A; (4) C; (5) A; (6) C;(7) A; (8) A; (9) C.
2.(1)三阶;(2) y=Y-'+c;(3)(4)
y =。-* + C x x + G ;
(5)y = -sin x + C}x + C2; (6)y = — x2 +x + 1 ; ( 7 ) Cj = 0,
C2 = 1 ;2
(8 ) '⑴ + 2/⑴=2x ?
1 /(0) = 0 *
(9) 〃=3;(10) x + xy?, = 0
3.(1) 一阶;(2) 一阶;(3) 一阶;(4)二阶;(5) 二阶。
4.(1)通解;(2)特解;(3)通解;(4)不是解。
C 1 3 5
□ ? y = -x - x --.
, 3 3
习题6.2
1.(1) B; (2) D; (3) C; (4) B; (5) C.
2.(1) y' + P(x)y = Q(x) ; (2) y = j Q(X)」P‘W*+ C ; (3)
V ) arcsiny = x + C ;
(4)y = Ce~';(5)y = b(x + C); (6)y = Y(x) + y*;
(7)
P(x) = xe^x一x ;
x = _L,x = Cv/_y。
3.
(1)”=睥、。;(2)),=峪;(3)),= 土;(4)arc tan y = arctanx + C;
2 ,Vl + x2
(5)tanxtany = C ; (6)(e x + 1)(^' - 1)= C;(7)y = Ce^yx;
(8)
A; (10)y = g-g"(x + C);(11) y = .v(- 2xln x + 2x
+ C);
(13) y2=2x2 Inx + 2Cx2;(14) y2 = 2x2 In x + 2Cx2 o
3.(1) W°;(2)cosy = ^COS A-.(3)y = 4;(4)ln),= ii^
2 1 - cosx
(5 ) cos y = - (e x + 1);
4
(6)),=工;(7))=必—);(8)+2);(9)COSX
(10)y = l-l + ±.
2 x
习题6.3
1. (1) C; (2) C; (3) B; (4) B; (5) C; (6) A;
(7) C; (8) B; (9) A.
2. (1) y = C{y, + C2y2; (2)y = C, sin x + C2 cosx
;(3)y = C]L +C2e x;
(4)y = e"(G cos、/5x + C? sin VJx) ;( 5 ) y = C} + C2e~lx | ( 6) y
= -—e~x \
2
(7 ) ),〃-2y' + 5y = 0 ;( 8 ) y =
C x e3x ^C2e4x;( 9 ) y = C} (e x -x) + C2 (e~x - x) + x;
(10 ) p = 2,q = 2J(x) = x+l.
3. (1) >- = -(x + 3>-r + C r v2 + C2x + C3; (2)y = C{+C2e x --x2 -x; (3)
2
1 ?
~y~ =Gx+;
(4)y = C l(x-e~x)+C2;(5)y = C)+ C2e'x;(6)y = (Cj +C2x)e2x;
(7 ) y = C/-2+^)x +C2e~^}x;( 8 ) y = C,e2x +C2e3x;( 9 )
y = c.e2x +C,e3x --X-—;-5 50
(10)y = C{e x +C,e-2x
2 4
4# ( 1) y = r + 3x + 1 ;(2)y = -^e^ - —e a x2l)x + (2a - a2 -
2);
cr 2a 2a
(3)y2 = 16(x +1) J(4)y = 2e*+e”;(5)、= 6广-4厂”.
习题6.4
⑵
3.0.14346934
4.0.83579;0.73273;0.68424;0.68974;0.75004.
习题6.5
1. v = —
; 2. y = 2e x
-2x-2; 3? 7 = 20 + 80/状'
4. i = e~5
' 4- sin 5r - cos5r ; 5* 0.93677 % ; 6. x(ci - bx)b
= x Q
(a - bx 0
)h
e a,
o
复习题六
D ; (2) D ; (3) D ; (4) C ; (5) A ; (6) A ;
(8) C ; (9) A ; (10) B ;
D ; (12) C ; (13) C ; (14) A ; (15) Co 2. (1) y(x) = —(l + ^2
)ln(l + x 2
)-—x 2
+—; (2)
y =
e
2 2 2
(3)y = -e-'+C ;(4)y =(C, + C 2
x)e x
+ x ;(5)y = C }
cosx + C 2
sinx-2x ;
(6) y = l ; (7) y = C
iX
2+C 2;
(8) y = C,e c -x
o
3. (1) y = Ccosx ;(2)(1 + x 2
)(1 + y 2
) = 4 ;(3)arcsin J
- = In x + C ; (4)
A
y=e x2(x 2
+c);
(5 )' I 】;(6 ) y = xarctanx - - hi(l + x 2
) + C
lX + C.
; ( 7 )
1 + x-
2
~
y = C } In Ixl +C 2
;
(8 ) y = arcs in (C| e x
)+C 2
; ( 9 ) y = e~x
+e 2x
; ( 10 )
1. (1)
(7) A ; (11) P ‘ _ p(x)dx J Q(x)e J dx + C \