dV/dt = rate in - rate out = 0.12 - kV^2 subject to the boundary condition V(0) = 2.Hey everyone! I'm stuck on the following:
A person is trying to fill a bucket with water. Water is flowing into the bucket from the tap at a constant rate of 0.12 litres/sec. However there is a hole in the bottom of the bucket and water is flowing out of the bucket at a rate proportional to the square of the volume of water present in the bucket. If V(t) is the volume of water (in litres) present in the bucket at time t (in secs) and the bucket initially contains 2 litres of water, write down, but do not solve, the differential equation for V(t) along with its initial condition.
Okay here is what I have:
Rate leaving is proportional to (sorry don't know how to write the symbol here) , therefore:
or should it be
So with that I get a function:
Okay my question is am I right in putting the rate it's leaving straight into that equation?
Can I just then sub in for V?
Any help would be great!