y''+2y'-3y=0 y'(0)=1 y(0)=0取Laplace变换有[s^2Y(s)-sy(0)-y'(0)]+2[sY(s)-y(0)]-3Y(s)=0即s^2Y(s)-1+2sY(s)-3Y(s)=0Y(s)=1/(s^2+2s-3)=1/4[1/(s-1)-1/(s+3)]取逆变换有y(t)=1/4[e^(t)-e^(-3t)]