Suppose we have an inverted conical tank with height H and radius R Suppose fluid is flowing through a hole in the bottom with cross sectional area a with velocity given by V(t) = k [2 g h(t)]1/2
where h(t) is the height of fluid in the tank.
Find
the time required to empty the tank |
Solution to Conical Tank Problem
A Mixture Application A 50 litre tank is initially filled
with 10 litres of brine solution containing 20 kg of salt. Starting from time t=0, distilled water is poured into the tank
at a constant rate of 4 litres per minute. At the same time, the mixture leaves the tank at a constant rate of k^(1/2)
litre per minute,. The time taken for overflow to occur is 20 minutes. Find Q(t) the amount of salt in the tank 0 < t < 20 |
Solution to Mixture Problem
Using a Differential Equation to Prove an Identity
Using Power Series show the solution to
dy/dx + x = y
is y = 1 + x + Cex . Verify this result using an appropriate integrating factor |
Power Series Solution
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