I m trying to find a separable equation for
t(5y+8t)^7y′=y(5y+8t)^7+t^8
in the form v =F(t,v)
I m stuck on the (5y+8t)^7 I don t know how I can simplify this to get something like v=u/t
更新1:
the form should be v' = F(t,v)
Separable Equations?
2017-09-11 2:58 am
Hello,
I m trying to find a separable equation for
t(5y+8t)^7y′=y(5y+8t)^7+t^8
in the form v =F(t,v)
I m stuck on the (5y+8t)^7 I don t know how I can simplify this to get something like v=u/t
I m trying to find a separable equation for
t(5y+8t)^7y′=y(5y+8t)^7+t^8
in the form v =F(t,v)
I m stuck on the (5y+8t)^7 I don t know how I can simplify this to get something like v=u/t
回答 (1)
2017-09-11 3:21 am
✔ 最佳答案
v = y/t
y = vt
y' = v + v't
t(5y+8t)⁷ y' = y(5y+8t)⁷ + t⁸
t(5vt+8t)⁷ (v + v't) = vt(5vt+8t)⁷ + t⁸
t⁸(5v+8)⁷ (v + v't) = vt⁸(5v+8)⁷ + t⁸
(5v+8)⁷ (v + v't) = v(5v+8)⁷ + 1
v + v't = (v(5v+8)⁷ + 1) / (5v+8)⁷
v + v't = v + 1/(5v+8)⁷
v't = 1/(5v+8)⁷
v' = 1/(t(5v+8)⁷)
This is separable
收錄日期: 2021-04-24 00:41:07
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170910185823AA3QiVk