T: 8x+19
7x-2(4-2x)+6(5-x)-x+2-(6x+5) = 7x-8+2x+30+6x-x+2-6x-5 = 8x+19
Y: 56-8x
9-(-2-3x)+4(-x+6)-x+12-3(2x-3) = 9+2+3x-4x+24-x+12-6x+9 = 56-8x
Let

. Then

and

are two fundamental, linearly independent solution that satisfy


Note that

, so that

. Adding

doesn't change this, since

.
So if we suppose

then substituting

would give

To make sure everything cancels out, multiply the second degree term by

, so that

Then if

, we get

as desired. So one possible ODE would be

(See "Euler-Cauchy equation" for more info)
Answer:
(4,-7)
Step-by-step explanation:
The answer for A. Is Yes. For every number of cups, there is one height in centimeters. The answer for B. Is Yes. Each height in centimeters corresponds to one particular number of cups. Hope this helps.