Re: [理工] [工數]-ODE
※ 引述《wil0829ly (汪汪)》之銘言：
: Consider the differential equation
: dy 2
: x──-4x y +2ylny = 0
: dx
: Find an integrating factor ρ(x, y)
: so that the multiplication of the differential
: equation by ρ(x, y) yields an exact differential equation.
: 這題我是先把ρ(x, y)乘到ODE 所以ODE變exact
: 在用判別式讓他相等 可是我還是解不出來= =
: 另外一題
: The Bernoulli equation is in the form of
: α
: P(x)y'+Q(x)y = R(x)y , in which α is a constant.
: Please find the integrating factor u(x, y).
: -α
: (Hint: try u(x, y) = f(x)y )
: 這題我也是用跟上面一樣的方法 還是算不出來= =
: 請各位高手幫幫忙 感恩!!
Q(x) R(x) α
dy + ------ydx = ------y dx //同除以P(x)
P(x) P(x)
1-α -α α
令 v = y ,dv = (1-α)y dy //同除以y
1 Q(x) R(x)
--------dv + ------vdx = ------dx
(1-α) P(x) P(x)
Q(x)
I = exp[∫(1-α)------dx]
P(x)
1 -α Q(x)
u(x,y) = ------y exp[∫(1-α)------dx]
P(x) P(x)
--
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※ 編輯: honestonly 來自: 118.167.138.31 (04/08 17:31)
※ 編輯: honestonly 來自: 118.167.138.31 (04/08 17:33)
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