Re: [理工] [工數] ODE 一問 H大 請問~~~
※ 引述《topee (eason)》之銘言：
: dy 2y-x+5
: ---- = -----------
: dx 2x-y-4
: 請問這題 用你那方法也行嗎?
這題另 x = u + α 帶入 ODE
y = v + β
(2u + 2α - v - β -4)dv = (2v + 2β - u - α + 5)du
4α-2β = 8
2β-α = -5
3α = 3
α = 1
β = -2
(2u - v)dv = (2v -u)du
u
另 z = --- , u = zv , du = zdv + vdz 帶入ode
v
(2zv - v)dv = (2v - zv)(zdv + vdz)
2 2 2
2zvdv - vdv = 2vzdv + 2v dz - z vdv - zv dz
2
- dv -2vdz +z dv + zvdz = 0
z(zdv + vdz) - 2vdz - dv = 0
zd(zv) - 2vdz - dv = 0
恩...
有請高手了
不然就是中間步驟 有錯...
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