Atank holds 300 gallons of water and 100 pounds of salt. a saline solution with concentration 1 lb salt/gal is added at a rate of 4 gal/min. simultaneously, the tank is emptying at a rate of 1 gal/min. find the specific solution q(t) for the quantity of salt in the tank at a given time t.

The amount of salt in the tank changes with rate according to

which is a linear ODE in . Multiplying both sides by gives

so that the left side condenses into the derivative of a product,

Integrate both sides and solve for to get

Given that , we find

and we get the particular solution

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