For the differential equation

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

\dfrac{dy}{dt}=y^{2}-ky

, where

k

is a non-zero real parameter, the number and stability of equilibrium solutions depend on the value of

k

. For which values of

k

does the equation have exactly one stable equilibrium solution? (a)

k=0

only (b)

k>0

only (c) All real

k\neq 0

(d) All real

k

(including

k=0

)