[工數]-拉氏!!!~~ 幫忙看一下^^

[topee (eason)]

y"  +5y' +6y = f(t)   y(0)=y'(0)=0


f(t)=  -2   for 0 ≦ t ＜ 3

        0   for t ≧ 3


f(t)= L[u(t)-u(t-3)](-2)

        -2     2
     =  --- + ---e^-3s
         s     s


令Y= L[y]

            1        -2      2
    Y = ---------- (----  + ---e^-3s )
        (s+3)(s+2)    s      s

            -2             2
      =  ---------- + ------------e^-3s
        s(s+3)(s+2)   s(s+3)(s+2)

                   2          1                 1   1     2    1      1
      y = e^-2t - ---e^-3t - --- +  u(t-3)L^-1[--- --- + --- ----- - --- ]
                   3          3                 3   s     3  (s+3)  (s+2)

                                                                     t=t-3

                   2          1
        = e^-2t - ---e^-3t - ---
                   3          3

                    1    2
          + u(t-3)[---+ ---e^-3(t-3) -e^-2(t-3)]
                    3    3

幫忙看一下^^



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推 shinyhaung:有點寫錯f(t)=(-2)[u(t)-u(t-3)]≠L[u(t)-u(t-3)](-2)
→ shinyhaung:應該是L{f(t)}=L[u(t)-u(t-3)](-2)
→ topee:.........
→ topee:是喔 這樣 我了解了..那其他過程??
推 shinyhaung:其他沒錯~
→ topee:感謝S大提醒= =
推 SONGya168:格式請修正