请教大家一道微分题，多谢！(原题贴错了，现纠正）

醉酒当歌

请教大家一道微分题，多谢！(原题贴错了，现纠正）
3 V% \9 M- P) @7 O- W  t
d [(a+bx)c ] /dx = -kc +s
where: only x and c are unknown, others are all known,  requiire c = function of x, what is this function?

7 y* ^8 X( Z7 u( k3 X* a! T/ {  `多谢了！
2 u, v6 b3 W. Z# Q: B/ h
[ Last edited by 醉酒当歌 on 2005-4-4 at 11:33 AM ]

sindowa

d [(a+bx)c ] /dx = -kc +s

(a+bx)c  = (-kc +s)x
ac+bxc=-kxc+sx
(a+bx+kx)c=sx
+ J( j' Q! z6 a9 Sc=sx/(a+bx+kx)

十年移民路_

Solution:

From:  d{(a+bx)*C(x)}/dx =-k C(x) + s
, }* D. j; h; y5 gso:
: J) b0 S! D4 @" I
bC(x) + (a+bx) dC(x)/dx = -kC(x) +s
i.e.

(a+bx) dC(x)/dx  = -(k+b)C(x) +s
% v2 R4 f, j. L# Z/ Q
7 D# X" {. D# J$ W/ @0 k4 Q1 U
7 e5 Q* p1 d# x' }introduce a tranform: KC(x)+s =Y(x), where K=-(k+b)
# B% ^  {7 V! [" Kwhich means: KdC(x)/dx = dY(x)/dx or dC(x)/dx = (1/K)dY/dx
" t3 \- P* M+ @% xtherefore:

{(a+bx)/K} dY(x)/dx=Y(x)

- f# c% B$ I* g2 Z# z- L  Tfrom here, we can get:

dY(x)/Y(x) = [K/(a+bx)]dx  i.e. dY(x)/Y(x) = K/b {(a+bx)}d(a+bx)

) R  I4 D8 S" T& x* Tso that:   ln Y(x) =( K/b) ln(a+bx)
  r% v" G& b& @
this means:  Y(x) = (a+bx)^(K/b)
by using early transform, we can have:
" k+ l0 D- B$ W- K# p% ^
-(k+b)C(x)+s = (a+bx)^(k/b+1)

finally:

C(x)= -1/(k+b)*{[(a+bx)^(k/b+1)] - s)