利用拉氏变换解下列微分方程或微分方程组

1.s^2L-2sL+L=1/(s-1)
L=1/(s-1)^3
=(1/2)*[2/(s-1)^3]
y=L^(-1){(1/2)*[2/(s-1)^3]}
=(1/2)L^(-1)[2!/(s-1)^3]
=(1/2)(e^t)*t^2
(利用L^(-1)F(s-c)=e^(ct)f(t))
2.s^2L-1+3sL+L=3s/(s^2+1)
L=1/(s^2+3s+1)+3s/[(s^2+1)(s^2+3s+1)]
=1/(s^2+3s+1)+[(s^2+3s+1)-(s^2+1)]/[(s^2+1)(s^2+3s+1)]
=1/(s^2+3s+1)+1/(s^2+1)-1/(s^2+3s+1)
=1/(s^2+1)
y=L^(-1)[1/(s^2+1)]
=sint