Can anyone please help me to solve this?
Use separation of variable to solve the differential equation
(dP/dt)=k(M-P), where k and M are constants.
Use your answer to find [lim(t->infinity) Pt].
Thanks..
solve differential equation
2012-09-27 8:32 pm
回答 (1)
2012-09-28 2:27 am
✔ 最佳答案
dP/dt = k(M - P)dP/(M- P) = k dt
- d(M - P)/(M - P) = k dt
Integrating both sides
- ln (M - P) = kt + C
ln (M - P) = - C - kt
So M - P = e^(- C - kt)
M - P = A e^(-kt) where A = e^(-C)
P = M - Ae^(-kt)
When t tends to infinity, e^(-kt) tends to zero, so P = M.
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