- #1
highlander2k5
- 10
- 0
Can someone tell me if I did this right because my solution seems wrong, but I've done it a couple times and get the same answer. I'm given the following:
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.
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