Mathematics

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.