Solve the differential equation (dy/dx) e^x - (dy/dx) = y e^x , given x and y are greater/ equal to 2, and y(3)=2 .?

[匿名]

2017-05-30 5:12 am

Answer is 2(e^x -1)/(e^3 -1), don t know where to start

回答 (1)

用戶57802

2017-05-30 5:21 am

✔ 最佳答案

(dy/dx)( e^x - 1) = y e^x
dy/y = e^x/(e^x-1)
integrate both sides
ln(y) = ln[C(e^x - 1)]
y = C(e^x - 1)
y(3)=2 --->C=2/(e^3-1)
hence
y = 2(e^x -1)/(e^3 -1

👍 1 👎 0

收錄日期: 2021-04-24 00:28:48
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170529211253AA9ksiv

檢視 Wayback Machine 備份