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

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

step-by-step explanation: it is d

sorry

step-by-step explanation:

sorry, but im pretty sure its a now that i look at it

think the answer is 30 degrees. if not than it is 20 degrees. not 100% sure. let me know if it was right.

gill russ