Re: [理工] ODE
※ 引述《ntust661 (一千個傷心的理由)》之銘言：
: ※ 引述《aaa19891212 (是......大頭!!!!)》之銘言：
: : 請問各位大大
: : http://ppt.cc/9wVH
: : 卡住了= =
: : 想不出頭緒要怎麼解他~~~
: 4x y'' + 2y' + y = 0
: 2 1 1
: x y'' + ── x y' + ── y = 0
: 2 4x
: 1 1 α
: 1 - 2 α = ── , α = ── , Let y(x) = x z(x)
: 2 4
: 2 1 2
: => x z'' + x z + (── - α ) z = 0
: 4x
: -1/2
: Let x = t , β = -1/2
: 2 1 t 2 α 2
: => t z'' + t z' + (── (──) - (──) ) z = 0
: 4 β β
: 1/4 1 1
: y(x) = x { c1 J ( - ── ) + c2 Y ( - ── ) }
: -1/2 x -1/2 x
真漂亮 那我補另外一個
2(2xy''+y') + y
2√x(√x*y')' + y
y'' + 2 y = 0 then y=y(√x)
∴y = c cos√2*√x + c sin√2*√x
1 2
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