Re: [工數] 微分方程一題
※ 引述《sukaxon (skx)》之銘言：
: 大家好
: 想請教微分方程一題
: y''+2y' = 2x+5-e^(-2x)
: 謝謝！
(D^2 +2D)y =2x+5-exp(-2x)
D(D+2)y = 2x+5-exp(-2x)
yh= C1 + C2exp(-2x)
1
yp= ─── [2x+5-exp(-2x)]
D(D+2)
1 1
= ───(2x+5) - ─── exp(-2x)
D(D+2) D(D+2)
= 0.5x^2 +2x +0.5xexp(-2x)
y=C1+C2exp(-2x)+0.5x^2+2x+0.5xexp(-2x)
--
Logic can be patient for it is eternal. ----- Oliver Heaviside
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 111.185.133.106
※ 文章網址: http://www.ptt.cc/bbs/Math/M.1415581449.A.DE3.html
推
11/10 14:22, , 1F
11/10 14:22, 1F
推
11/10 15:37, , 2F
11/10 15:37, 2F
推
11/10 15:57, , 3F
11/10 15:57, 3F
推
11/10 16:09, , 4F
11/10 16:09, 4F
→
11/10 16:10, , 5F
11/10 16:10, 5F
→
11/10 17:41, , 6F
11/10 17:41, 6F
→
11/10 17:43, , 7F
11/10 17:43, 7F
推
11/10 19:09, , 8F
11/10 19:09, 8F
→
11/10 19:09, , 9F
11/10 19:09, 9F
→
11/10 19:49, , 10F
11/10 19:49, 10F
→
11/10 19:51, , 11F
11/10 19:51, 11F
推
11/10 20:07, , 12F
11/10 20:07, 12F
→
11/10 20:48, , 13F
11/10 20:48, 13F
討論串 (同標題文章)