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

  1. May 18, 2009 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    none

    3. 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
     
  2. jcsd
  3. May 18, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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?
     
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