[工數] laplace
問題一
y"+4y=4cost , if 0<t<π , and 0 if t>π
[ s^2 Y - sy(0) - y'(0) ] + 4Y = 4s/(s^2+1)
這邊我就有小問題了 y(0)=? y'(0)=? 題目少給吧@@?
問題二
y"+2y'+2y=r(t)
r(t)=10sin2t if 0<t<π and 0 if t>π
y(0)=1 , y'(0)=-5
最後算出來 y=[ e^(-t) ]*[cost-4sint]
- 2cos2t -sin2t + [e^(-t)]*[2cost+4sint]
+ 2cos2t +sin2t + [e^(-t+π)]*[2cost+4sint]
答案是分段討論的 我不懂怎麼分 ~"~
y=3[e^(-t)]*cost -2cos2t -sin2t
if 0<t<π
y=[e^(-t)]*{ [3+2(e^π)]cost + 4(e^π)sint }
if t>π
先感謝版內的大大們了 我卡了好久 >"<
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