利用拉氏变换解下列微分方程或微分方程组

1个回答

  • 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