I'll do the math for this, it may take me a few minutes so i will update this comment with an answer in just a minute. I always get anxious when nobody replies kind of quickly as i feel it is being forgotten. So just a heads up i'm working on a answer!
Answer:
equal to
Step-by-step explanation:
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)
9514 1404 393
Answer:
5 hours
Step-by-step explanation:
The volume of the pool is ...
V = LWH
V = (10 ft)(8 ft)(5 ft) = 400 ft^3
At the given fill rate, the time it will take is ...
(400 ft^3)/(80 ft^3/h) = 5 h
It will take 5 hours for the pump to fill the pool.