※ 引述《semmy214 (黃小六)》之銘言:
: https://imgur.com/a/ESOiOse
: dy=-e^-x*y^2dx+ydx+e^xdx
: 乘完後就不知怎麼下手~
: 求高手協助~
另解:
y' = -exp(-x)y^2 + y + exp(x)
顯然y = exp(x)是一解
y = exp(x) + 1/z
y' = exp(x) - z'(1/z^2)
=> z' - z = exp(-x)
=> [exp(-x)z]' = exp(-2x)
=> z = (-1/2)exp(-x) + Aexp(x)
=> y = exp(x) + 2/[Bexp(x) - exp(-x)]
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 61.56.10.112
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1539572867.A.400.html