Alex Aka alex
New member
A tank initially contains 30 kg of salt disolved in water and making up 4000 litres of liquid.
Brine that contains 30 grams of salt per litre of solution enters the tank at a rate of 25 litres per minute.
The solution is kept thoroughly mixed and drains from the tank at the same rate.
Let y(t) denote the amount of salt (in kg) after t minutes.
Modelling the situation by a differential equation, beginning,
dy/dx = RateSaltComesIn - RateSaltGoesOut
it can be shown that y(t) satisfies an initial-value problem of the form:
dy/dt + ay = b, y(0) = y0
What are the numeric values of a, b and y0?
Brine that contains 30 grams of salt per litre of solution enters the tank at a rate of 25 litres per minute.
The solution is kept thoroughly mixed and drains from the tank at the same rate.
Let y(t) denote the amount of salt (in kg) after t minutes.
Modelling the situation by a differential equation, beginning,
dy/dx = RateSaltComesIn - RateSaltGoesOut
it can be shown that y(t) satisfies an initial-value problem of the form:
dy/dt + ay = b, y(0) = y0
What are the numeric values of a, b and y0?