Testing Stability of Linear System Fixed Points

[coverband]

Homework Statement

Classify the fixed points of the following linear system and state whether they are stable or unstable

$$\dot{x}=x + y$$
$$\dot{y} = x + 3y$$

Homework Equations

The Attempt at a Solution

Fixed point at dy/dx = 0/0. Therefore fixed point = (0,0)

How does one test for stability?

Thanks

 

[Mark44]

Homework Statement

Classify the fixed points of the following linear system and state whether they are stable or unstable

$$\dot{x}=x + y$$
$$\dot{y} = x + 3y$$

Homework Equations

The Attempt at a Solution

Fixed point at dy/dx = 0/0. Therefore fixed point = (0,0)

How does one test for stability?

Thanks

0/0 is not a number, so how can you say that there is a fixed point at dy/dx = 0/0?

 

[coverband]

How does one test for stability?

 

[LCKurtz]

How does one test for stability?

Doesn't your text have a test for stability which involves looking at the eigenvalues of the coefficient matrix on the right side?