Screenshоt 2024-11-02 13.57.16.png A 300 liter tаnk initiаlly cоntаins 3 kg оf dye dissolved in 200 liters of water. A dye solution containing $$2$$ kg of dye per liter flows into the tank at the rate of 4 liters per minute, while pure water flows in a separate pipe at 5 liters per minute. The well-mixed solution is drawn off at the rate of 7 liters per minute. (a) Set up an initial value problem for $$V(t)$$, the volume of dye solution in the tank after $$t$$ minutes, and then find $$V(t)$$. (b) Set up, but do not solve, an initial value problem for $$x(t)$$, the mass of dye in the tank after $$t$$ minutes. Classify the resulting differential equation.