怎么用拉普拉斯变换求解微分方程?题目：dx/dt=x-2y,dy/dt=5x-y;x(0)=-1,y(0)=2

做Laplace变换得sX(s)-x(0)=X(s)-2Y(s),sY(s)-y(0)=5X(s)-Y(s).
解得X(s)=-(s+5)/(s^2+9)=-(s/(s^2+9)+(5/3)*3/(s^2+9)),
Y(s)=(2s+3)/(s^2+9)=(2s/(s^2+9)+3/(s^2+9))
查表得
x(t)=-(cos3t+5/3sih3t)
y(t)=2cos3t+sin3t