Re: 工數] 一階線性常微分方程式求解

看板Math作者Heaviside (Oliver)時間10年前 (2015/11/06 23:50)推噓8(8推 0噓 3→)

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※ 引述《DEARSOL (SOL)》之銘言： : http://i.imgur.com/l4UzaoD.jpg

: 解到這邊卡住了 : 無法分部哪裡出了問題呢? dy +tan(x)ydx = (cosx)dx sin(x) dy + ─── y dx = (cosx)dx cos(x) cos(x)dy- yd[cos(x)] = (cosx)^2 dx cos(x)dy-yd[cos(x)] ────────── = dx (cosx)^2 y y d(──) =dx => ─── = x+k => y=xcos(x)+kcos(x) , K=const cosx cosx ※另解 y' +tan(x)y =cos(x) let P(x)=tan(x), Q(x)=cos(x) I(x)=exp(∫P(x)dx)=exp(∫tan(x)dx)=sec(x) I(x)y(x) = ∫I(x)Q(x)dx +k , k=const sec(x)y(x)= ∫sec(x)cos(x)dx +k sec(x)y(x) = ∫dx +k sec(x)y(x)= x+k y(x) = x(cosx) + kcos(x) -- Logic can be patient for it is eternal. ----- Oliver Heaviside -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 114.32.247.47 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1446825008.A.14D.html ※ 編輯: Heaviside (114.32.247.47), 11/06/2015 23:58:09

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D1004323038

11/07 00:36, , 1^F

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softseaweed

11/07 01:44, , 2^F

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DEARSOL

11/07 19:59, , 3^F

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