→ wanderer:二神PK~~ 推 140.112.18.99 10/20
※ 編輯: JGU 來自: 61.230.36.226 (10/20 22:03)
Why does f have to be in the form e^(ax) ?
I think that's the major problem when solving homogeneous linear ODE....
※ 引述《kafai (雲^^)》之銘言：
: the followings phi noted as f
: since f'' + k^2 * f = 0 (*)
: let f = e ^ (ax)
: so a^2 * e^(ax) + k^2 * e^(ax) =0
: => a = +/- ki
: then we have
: f = A * e^(ikx) + B * e^(-ikx)
: = A * ( cos(kx) + i * sin(kx) ) + B * ( cos(-kx) + i * sin(-kx) )
: = A'* cos(kx) + B'* sin(kx) ( A' = A+B ; B' = i*(A-B) )
: since f(0)=0,
: f(0) = A' = 0
: f = B' * sin(kx)
: i.e. phi = A * sin(kx)
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