Separable Equations?

👨🏻‍🏫 學術台數學

[匿名]

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

更新1:

the form should be v' = F(t,v)

回答 (1)

用戶48544

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

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