Examples of Slope Fields

dy/dx = x2 − y2

dy/dx = x^2 - y^2

dy/dx = x − xy:   solution curves y = ce−x2/2 + 1

dy/dx = x - xy

dy/dx = y2 − 3y:   y = 0 is stable (attractor), y = 3 is unstable (repeller)

dy/dx = y^2 - 3y

dy/dx = y2(2 − y):   y = 0 is semi-stable, y = 2 is stable (repeller)

dy/dx = y^2(2-y)

Images generated by sage.