Consider the differential equation dy/dx = 2 − y.
(a) Either by inspection or by the concept that
y = c, −[infinity] < x < [infinity],
is a constant function if and only if
y' = 0,
find a constant solution of the DE.
y =
(b) Using only the differential equation, find the intervals on the y-axis on which a nonconstant solution
y = ϕ(x)
is increasing. Find the intervals on the y-axis on which
y = ϕ(x)
is decreasing. (Enter your answer using interval notation.)
increasing
decreasing