Consider the differential equation dxdy=y(1−y) with equilibrium solutions at y=0 and y=1. Which statement most accurately describes the behavior of the solution curve that passes through the point (0,2) as x increases?
a) The curve decreases and crosses y=1 since the slope there is negative, continuing downward afterward.
b) The curve decreases and approaches y=0, leveling off without crossing that line.
c) The curve decreases and approaches y=1, leveling off without crossing that line.
d) The curve increases without bound because dxdy is always positive when y>0."