Section $7\mathrm{.}6-$ Systems of Linear Differential Equations

Name:

$3.$ When the Laplace transform is applied to the system

$\frac{dx}{dt}=3x-y$

$\frac{dy}{dt}=xy$

$x(0)=2,y(0)=1$

the resulting transformed system is

Possible answers.

a$.$ s$x=3x-Y-2,sY-1=xY$

b$.sx-2=3x-Y,sY=x+Y-1$

c$.sx=3x-Y-2sY=x+Y-1$

d$.sx-2-3x-Y,sY-1-x+Y$

e$.$s$x+2-3x-sY,Y+1-x+Y$

$4.$ The solution of the system in the previous problem is

Possible answers.

a$.x=2e^{2t}t{e}^{2t},y=e^{2t}t{e}^{2t}$

b$.x=2e^{2t}t{e}^{2t},y=e^{2t}-t{e}^{2t}$

c$.x=2e^{2t}t{e}^{2t},y=e^{2t}t{e}^{2t}$

d$.x=2e^{2t}-t{e}^{2t},y=e^{3t}-t{e}^{2t}$

c$.x=2e^{2t}t{e}^{2t},y=e^{2t}-t{e}^{2t}$