Mathematics

Problem

For the differential equation

\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

)