Re: [理工] [工數]-一階ODE
※ 引述《ecko1023 (NEIGHBORHOOD)》之銘言：
: dy xy^2-cosx sinx
: ---- = ------------------ y(0)=2
: dx y(1-x^2)
: 有請神人了!!
: 我這題算超久...
2
xy - cosx sinx
y'=----------------
2
y ( 1 - x )
2 2
( x y - y ) dy + ( xy - cosx sinx ) dx = 0
因d(xy) = x dy + y dx
原式可化為
1
(xy) d(xy) - y dy - --- sin2x dx = 0
2
1 2 1 2 1
---(xy) - --- y + --- cos2x = c'
2 2 4
2 2
2(xy) - 2y + cos2x = c
代入IC y(0) = 2
0 - 8 + 1 = -7 = c
2 2
2(xy) - 2y + cos2x + 7 = 0
--
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◆ From: 58.114.170.39
※ 編輯: youmehim 來自: 58.114.170.39 (07/22 12:39)
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