MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A differential equation is given by dxdy=y−2. A student wishes to reason about its solutions by examining a slope field.
(a) Identify every point in the xy-plane at which the slope indicated by the differential equation is zero.
(b) Describe how the set of points you found in part (a) would appear on a slope field and explain what this visual feature tells you about the family of solution curves.
(c) Without solving the differential equation, explain how the magnitude and sign of the slopes change as the y-coordinate moves farther above 2 and farther below 2, respectively. Justify your conclusions verbally.