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

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w