Re: [微積] 微積分兩題疑問
: 第一題 跟 第六題
: 我算的結果分別如圖
: 但是第一題t=2代入後讓我很困擾
(t^2 - 1)y' = y^2 - 1
=> ∫[1/(y^2 - 1)]dy = ∫[1/(t^2 - 1)]dt
=> (1/2)ln|(y - 1)/(y + 1)| = (1/2)ln|(t - 1)/(t + 1)| + C
y(2) = 1/2
(1/2)ln|-1/3| = (1/2)ln|1/3| + C
=> C = 0
=> -(y - 1)/(y + 1)| = 9/11
=> 11(y - 1) = -9(y + 1)
=> y(10) = 1/10
: 至於第六題，我不知道它像是哪種的泰勒展開形式
y"(t) = 4y(t)
y(0) = 1
y'(0) = -2
y"(0) = 4
y"'(0) = -8
∞
y(t) = Σ [(-2)^k t^k]/(k!)
k=0
= exp(-2t)
: 有請版上的超人解答了!!!
: 大恩不言謝!!!
: 嗚嗚嗚嗚~~
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 111.249.190.66
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1497880294.A.5BC.html
→
06/19 22:10, , 1F
06/19 22:10, 1F
→
06/19 22:10, , 2F
06/19 22:10, 2F
推
06/20 00:59, , 3F
06/20 00:59, 3F
推
06/20 01:45, , 4F
06/20 01:45, 4F
→
06/20 01:45, , 5F
06/20 01:45, 5F
討論串 (同標題文章)
