Which statement correctly defines an equilibrium solution of the first-order…

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

Problem

Which statement correctly defines an equilibrium solution of the first-order differential equation

\dfrac{dy}{dt}=f(t,y)

? (a) An individual point

(t_0,y_0)

where

f(t_0,y_0)=0

.},{ (b) A solution of the form

y=c

for which

f(t,c)=0

for every value of

t

.},{ (c) A solution curve that passes through the origin and has zero slope there. (d) Any value of

t

at which the function

y(t)

attains a local maximum or minimum.