phase portrait direction clockwise or anticlockwise?

pashkar

hi i would like some steps to help determine whether my unstable spiral is anticlockwise or clockwise.

i have the slope equation of dY/dX=( -4x +y)/y.

iv tried subbing in x = 0 and y = 0, but it really doesnt help me understand the direction of the spiral.
please list some easy steps/ methods to work out direction. i'd really appreciate it. cheers

HallsofIvy

You need to look at dy/dt and dx/dt separately. What are the original equations?

For example dy/dt= -4x+ y, dx/dt= y and dy/dt= 4x- y, dx/dt= -y both give
dy/dx= (-4x+ y)/y- their phase portraits will be identical but they will be "traversed" in opposite directions. Looking at x= 0, y= 1, dy/dt= 1, dx/dt= 1 for the first so the "motion" is clockwise. But dy/dt= -1, dx/dt= -1 for the second so the "motion" is anti-clockwise.