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

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Homework Statement

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

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

The Attempt at a Solution

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

How does one test for stability?

Thanks

Mentor

Homework Statement

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

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

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?