Consider the family of differential equations parameterized by the real constant

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Consider the family of differential equations

\dfrac{dy}{dx}=(y-k)(y-2k)

parameterized by the real constant

k

. Identify all values of

k

for which the slope field possesses exactly one stable equilibrium solution, and state which equilibrium that is.