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）
  v- [4 Y9 ], q- @( A* [
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?
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# H5 }: `+ L4 O6 h- ~9 U; I  s多谢了！

! ?; P4 m! k) |( F9 K6 R[ Last edited by 醉酒当歌 on 2005-4-4 at 11:33 AM ]

sindowa

d [(a+bx)c ] /dx = -kc +s
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: R0 ~0 |: ^( z3 j+ ?(a+bx)c  = (-kc +s)x
ac+bxc=-kxc+sx
(a+bx+kx)c=sx
# U5 w0 r! H+ L6 s) q6 U5 W! zc=sx/(a+bx+kx)

十年移民路_

Solution:
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2 F+ M7 A- o$ Q0 F! u, R9 `From:  d{(a+bx)*C(x)}/dx =-k C(x) + s
( N7 n* [/ k( u) k/ rso:
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bC(x) + (a+bx) dC(x)/dx = -kC(x) +s
i.e.
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(a+bx) dC(x)/dx  = -(k+b)C(x) +s

- ?' c" @5 B$ c0 l; u0 v! G
6 ?0 T& |  k5 y4 I) h6 |. Xintroduce a tranform: KC(x)+s =Y(x), where K=-(k+b)
which means: KdC(x)/dx = dY(x)/dx or dC(x)/dx = (1/K)dY/dx
/ q3 g( u( b  D; {, n1 xtherefore:

{(a+bx)/K} dY(x)/dx=Y(x)
2 c7 `7 i- U: k7 v
from here, we can get:
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1 o: S/ i% t/ B* O* X, Y( ndY(x)/Y(x) = [K/(a+bx)]dx  i.e. dY(x)/Y(x) = K/b {(a+bx)}d(a+bx)

so that:   ln Y(x) =( K/b) ln(a+bx)

this means:  Y(x) = (a+bx)^(K/b)
by using early transform, we can have:

0 _$ J6 F7 p" u4 @) B% ?-(k+b)C(x)+s = (a+bx)^(k/b+1)
, _! L" T2 l, ?8 m5 f! F9 a
finally:

, S; H# l& ]# R- TC(x)= -1/(k+b)*{[(a+bx)^(k/b+1)] - s)