Re: [理工] [理工]-ODE
※ 引述《ntust661 (661)》之銘言:
: y'' + y = secx
: yh = c1 cosx + c2 sinx
: yp = ψ1 cosx + ψ2 sinx
: W = 1
: ψ1 = -∫ secx sinx dx
: = - ∫ tanx dx
: = ln cos x
: ψ2 = ∫ secx cosx dx
: = ∫ dx
: = x
: yp = ln │cosx│ cosx + x sin x
: Y = yh + yp
: = c1 cosx + c2sinx + ln │cosx│ cosx + x sin x
: 根本沒有那種詭異的積分吼= =
原來是這樣阿
我都是參數變異法慢慢做
yp = ψ1*y1 + ψ2*y2
y'p = ψ'*y1 + ψ'*y2 + ψ1*y'' + ψ2*y''
1 2
取
ψ'*y1 + ψ'*y2 = 0
1 2
y''p = .....
然後帶入ODE
ψ'*y1 = -ψ'*y2
1 2
這樣慢慢解@@
你的方法太快了 如果題目規定
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