Hey guy, I'm having a problem with First order ODE (again)
The Melting Pot. A tank containing 20,000 litre of blended fuel oil is stirred continuously to keep the mixture homogeneous. The Fuel is blended from a heavy and a light component in equal proportions. The two components are added at a rate of 5 litres/min each, then the blended fuel oil is withdrawn at a rate 10 litres/min to be burnt in a furnace. The blended fuel oil will not burn in the furnace if the heavy component forms more than 80% of the mixture
At a certain instant, the supply of the light component ceases whilst the heavy component continues to be added at the same rate of 5 litres/meter and the homogeneous mixture is withdrawn at the same rate of 10 litres/min.
a) let x(t) be the amount of heavy fuel in the tank (in litres) at time t minutes after the supply of light oil ceases. Show that
The only problem in question a) I encounter is the "-5*t" can any one tell me where it comes from?
b) Solve this differential equation for x(t)
This is my working out for this part
I got an answer of
but the answer in the worksheet is
Can any one tell me where I went wrong?