Let be the amount of salt at time .A tank contains a perfectly mixed solution of 5kg of salt and 500 litres of water. Starting at t=0, fresh water is poured into the tank at a rate of 4 litres/min. A mixing device mainntains homogeneity. The solution leaves the tank at a rate of 4 litres/min.

a). What is the differential equation governing the amount of salt in the tank at any time?

This means,

The rate (of salt) in is 0 since only clean water is coming in.

The rate (of salt) out is .

Thus,