Find the type of equilibrium at (0,0) for x'=x, y'=y

[anicic]

Homework Statement

I need to solve the differential equations given, find the type and stability of the equilibrium at (0,0), without matricies.

Homework Equations

none

The Attempt at a Solution

starting:

x' = x
y' = y

dy/dx = y'/x' = y/x

=> dy/y = dx/x

integrating gives

ln y + c1 = lnx + c2

rearrange and get

ln(y/x) = c


have i done it right so far?
i get stuck at this point

 

[HallsofIvy]

I'm only wondering why you are solving for y as a function of x at all.

dx/dt= x, dy/dt= y. What is true about the derivatives if x and y both close to 0 but positive?