※ 引述《shinycc (大大baby和多多baby)》之銘言：
: A tank contains 200 gal of water in which 40 lb of salt are dissolved.Five gal
: of brine each contains 2 lb of dissolved salt,run into the tank per minute,and
: the mixture,kept uniform by strring,runs out at the same rate.Find the amount
: of salt y(t) in the tank at any time t
: 求教各位高手 Orz
_______ when t=0 V=200gal
5gal/min=>│ │ θ=40/200 lb/gal
(2lb/gal) │ tank│
│_____│===>5gal/min
令tank內brine的濃度θ=lb/gal
d(VQ)/dt=5.2-5θ θ(0)=0.2
d(200θ)/dt10-5θ dθ/dt=1/20-θ/40 dθ/dt=-(θ-2)/40
dθ/(θ-2)=-dt/40 假設少θ=2之解
d(θ-2)/(θ-2)=-dt/40 ln│θ-2│=-t/40+lnc
θ-2=ce^-t/40 θ=ce^-t/40 +2
代入t=0 θ=0.2 的c=-1.8 y=Vθ=200(2-1.8e^-1/40)
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※ 編輯: inoran54787 來自: 140.122.32.240 (05/01 20:08)