埃德蒙顿华人社区-Edmonton China

 找回密码
 注册
查看: 1767|回复: 2

请教大家一道微分题,多谢!(原题贴错了,现纠正)

[复制链接]
鲜花(150) 鸡蛋(3)
发表于 2005-4-3 19:44 | 显示全部楼层 |阅读模式
老杨团队,追求完美;客户至上,服务到位!
请教大家一道微分题,多谢!(原题贴错了,现纠正)( Z: h1 P$ k6 @8 o: W2 k: g
4 K1 ?/ W+ \  h# F) z
d [(a+bx)c ] /dx = -kc +s ( F5 p! j9 i1 g7 w7 T! {" `
where: only x and c are unknown, others are all known,  requiire c = function of x, what is this function?- ]: |6 |, V( H; p8 Q! N

6 E4 o: C5 H& g多谢了!7 i& m* h& e2 P0 J" P

( N! x' m7 N- u" W[ Last edited by 醉酒当歌 on 2005-4-4 at 11:33 AM ]
鲜花(0) 鸡蛋(0)
发表于 2005-4-5 02:47 | 显示全部楼层

供参考

d [(a+bx)c ] /dx = -kc +s
/ X+ N+ o4 V( y7 r' o- b) H$ o7 A1 M* B, i2 f
(a+bx)c  = (-kc +s)x
# \% Z$ X4 D3 B4 W% L- |, R4 qac+bxc=-kxc+sx) r: u# T- f0 M; r  f2 M) x5 X9 `
(a+bx+kx)c=sx. H# \9 G" |- B# [9 U
c=sx/(a+bx+kx)
鲜花(19) 鸡蛋(0)
发表于 2005-4-5 22:11 | 显示全部楼层
Solution:
* f1 i9 N* R& w! v7 K' L3 i- K: J8 t8 p
From:  d{(a+bx)*C(x)}/dx =-k C(x) + s$ y4 u. t% H( T' o$ Z+ t2 I8 f
so:9 p. Z+ c+ D1 y  Y

1 g- e# f6 q7 [! g) L% ibC(x) + (a+bx) dC(x)/dx = -kC(x) +s
3 a8 r4 _# ?  ]  o/ [i.e.% H* [7 n* {% N- }9 n: F; I
. ^' \* E9 o% E: E. M4 S
(a+bx) dC(x)/dx  = -(k+b)C(x) +s
& w  g" B+ s3 J$ L7 }0 N: ~/ O7 c8 p: Y0 a* P% E

# p; j' H9 T4 I" B2 @introduce a tranform: KC(x)+s =Y(x), where K=-(k+b)   e" P% g+ r( C8 l, q' N7 y! E
which means: KdC(x)/dx = dY(x)/dx or dC(x)/dx = (1/K)dY/dx0 ?* g$ k: U0 j
therefore:2 c& J! S% w9 J( a6 c4 E

4 v/ S7 x3 d. K/ R. |9 B$ _{(a+bx)/K} dY(x)/dx=Y(x)$ D% L3 j  E$ ~) {8 e% V
5 A2 O" d* b# I4 K4 G2 E
from here, we can get:6 |+ S: }/ N( e' j- O/ n: G

, m1 D% \  H) h3 y: g3 w6 D+ ^, ~dY(x)/Y(x) = [K/(a+bx)]dx  i.e. dY(x)/Y(x) = K/b {(a+bx)}d(a+bx)
- m' L$ q. Y0 X, x# c/ A! J, U! T+ [
, j' v/ l4 h+ `! k: aso that:   ln Y(x) =( K/b) ln(a+bx), z% q) T+ r; a- H
7 a  E6 `) E) O& |. D
this means:  Y(x) = (a+bx)^(K/b)
+ _0 l6 N, E9 pby using early transform, we can have:
( e& C) o/ M) ~7 f0 g
- w$ D& o2 B( c  a-(k+b)C(x)+s = (a+bx)^(k/b+1)) x8 n! \: R- \% Z

# a6 L0 w1 ], }$ P. cfinally:8 \& \1 ^1 u+ X3 `8 Z

" f& e' {) d% C# ~# PC(x)= -1/(k+b)*{[(a+bx)^(k/b+1)] - s)
您需要登录后才可以回帖 登录 | 注册

本版积分规则

联系我们|小黑屋|手机版|Archiver|埃德蒙顿中文网

GMT-7, 2025-11-18 01:51 , Processed in 0.138057 second(s), 14 queries , Gzip On, APC On.

Powered by Discuz! X3.4

Copyright © 2001-2021, Tencent Cloud.

快速回复 返回顶部 返回列表