※ 引述《kyod (Kiss you on dark...)》之銘言：
: Use Laplace Transformation(with respect to t) to solve the partial
: differential equation.
: ytt(x,t) = a^2 yxx(x,t) - g , where a and g are constants ;
: and y(x,t) satusfies the boundary conditions y(x,0) = yt(x,0) = 0 ,
: y(0,t) = 0 , lim yx(x,t) = 0 .
: x-> 無窮大
: 答案: y = g H(t-x/a) * 1/2 * (t-x/a)^2 - g * 1/2 * t^2
:
雖然原po已經解決了
不過基於好奇心下我也解了這題
此時卡題 希望有高手幫解惑 ..
2 d 2 g
a ----L[y(x,t)] = s L[y(x,t)] + ---
dx s
2 d 2 g
a --- Y = s Y + ---
dx s
s 2 g
Y'' - (---) Y = ---
a s
x -x
---s ---s
a a g
Y = c1 * e + c2 * e - -----
sa^2
恩 .. 之後... 高手幫忙接續
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