I need this calculus 2 question answered reallt soon! I did it 4 times and I still havent gotten the answer

Question

A tank contains 400 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. If y(t)

 is the amount of salt (in kilograms) after t minutes, show that y satisfies the differential equation

dy

dt

= 2 − 3y

400 + 2t

.

Solve this equation and find the concentration after 20 minutes. (Round your answer to four decimal places.)

Answer 1

dy/dt = 2 - 3y/(400 + 2t); dy/dt + 3y/(400 + 2t) = 2. Integrated factor M = e^{∫3/(400 + 2t)dt} = e^{3/2ln(400 + 2t)} =

(400 + 2t)^3/2; d/dt((400 + 2t)^3/2y) = 2(400 + 2t)^3/2; (400 + 2t)^3/2; y(t) = 4/5(400 + 2t) + C(400 + 2t)^-3/2;

y(0) = 4/5·400 + C·400^-3/2 = 0; C = - ·320·400^3/2 = - - 2560000

y(t) = 4/5(400 + 2t) - 2560000(400 + 2t)^-3/2;

y(20) = 4/5(400 + 40) - 2560000(400 + 40)^-3/2 = 162.6291 kg

concentration ρ(20) = y(20)/(400 + 40) = 0.3696 kg/L