Question

Solve the differential equation.

Answer 1

A large tank is initially filled to capacity with 10 gallons of saltwater solution that has a
salt concentration of 2 lbs/gallon. A saltwater solution containing 3 lbs of salt per gallon
is pumped into the tank at a rate of 2 gal/min. The well-mixed solution is pumped out
of the tank at the rate of 3 gal/min.

Set up a differential equation for y(t), the amount of salt water in the
tank after t minutes have elapsed. Also specify the initial condition.

Solve the differential equation. Your answer should not have any unspecifed constants in it.

Answer 2

Heres what i have:
V(0) = 10 gal
V(t) = 10-t
y(0) = 20
y(t) = ???
in(t) = 2 gal/min
out(t) = 3 gal/min
k(t) = 3 lbs/gal

Answer 3

i solved the entire equation after hours of labor, and my final equation for y(t) is...

y(t) = \[(t+10)^{3}(\frac{ -3 }{(t+10)^{2} }+ \frac{ 1 }{ 20 })\]

Answer 4

when i solved for my constant i got 1/20