- #1

highlander2k5

- 10

- 0

x' + 2y' + x = 0

x' - y' + y = 1

and the initial values of x(0) = 0 and y(0) = 1

The idea is to solve this initial value problem.

Can someone please tell me if this is right? Thanks.Here's my work.

Start by taking laplace transforms, so:

sX + 2sY - 2 + X = 0

sX - sY + 1 + Y = 1/s

D = | s+1 2s | = -3s^2 +1

| s -s+1 |

D_x = | 2 2s | = 0

| 1/s - 1 -s+1 |

D_y= | s+1 2 | = -3s^2 +1 / s

| s 1-s/s |

In between the | | are values to take cross product.

Then use Cramer's Rule.

X(s) = D_x / D = 0/-3s^2 +1 = 0

Y(s) = D_y / D = -3s^2 + 1 / s(-3s^2 + 1) = 1/s

then take the laplace transforms and I get x(t)=0 and y(t)=1