※ 引述《redpig (耶耶耶~)》之銘言:
: ※ 引述《deathcustom (我一定會討回來)》之銘言:
: : dZ/dt + Z = 1 + t
: : let Zh = exp(at)
: : a exp(at) + exp(at) = 0
: : a = -1
: : let Zp = At + B
: : A + At + B = 1 + t
: : A = 1, B = 0
: : Z = CZh + Zp = Cexp(-t) + t
: : 以下的題目用同樣的方法
: 不好意思 想再請問一下
: 如果是 Z' = Z + exp(t) + sin(t)
: 那麼要怎麼設 Zp ?
: 謝謝大大~~
Method I
dz/dt - z = exp(t) + sin(t)
d(zexp(-t)) = exp(-t)[exp(t) +sin(t)]dt
zexp(-t) = t + ∫exp(-t)sin(t) dt
Method II
(D-1)z = exp(t) + sin(t)
(D^2+1)(D-1)^2 z = 0
z = Kexp(t) + Atexp(t) + Bcos(t) + Csin(t)
solve A, B, C
z' - z = Aexp(t) + Atexp(t) - Bsin(t) + Ccos(t) - Atexp(t) - Bcos(t) - Csin(t)
= exp(t) + sin(t)
A = 1
-B -C = 1
B = C = -0.5
z = Kexp(t) +texp(t) - 0.5(cos(t)+sin(t))
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