Re: [理工] [工數]-高階O.D.E. by 逆算子
※ 引述《ncuatm (VC #15)》之銘言：
: 1. y" + y = -2sinx + 4xcosx
: 答案: y = c1cosx + c2sinx + 2xcosx + x^2sinx
: 這題yp我算出來是xcosx + x^2sinx 看了好多遍都找不出錯誤原因...
: 2. y"- 3y' - 4y = x^-3 * exp(4x) * (5x-2)
: 答案: y = c1exp(-x) + c2exp(4x) - x^-1 * exp(4x)
: 3. y" + y = secx * tanx
: 答案: y = c1cosx + c2sinx - sinx * ln|cosx| + x * cosx
: 麻煩解惑 感謝
1. 1 1
Yp= ------- (-2sinx) + ------- 4xcosx
D^2+1 D^2+1
-xcosx 1 -2D
=-2 -------- + 4(x------- cosx + --------- cosx )
2 D^2+1 (D^2+1)^2
xsinx cosx 2
= xcosx + 4 [x(-------- + --------) + ---------- sinx ]
2 4 (D^2+1)^2
xsinx cosx 2
= xcosx + 4 [x(-------- + --------) + --------(-1) x^2sinx ]
2 4 8
= 2xcosx+ x^2sinx
應該是這樣!!
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◆ From: 112.104.109.34
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※ 編輯: kusorz 來自: 112.104.109.34 (08/09 18:56)
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