A tank contains 100 kg of salt and 2000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 13 L/min.
Let y be the number of kg of salt in the tank after t minutes.
The differential equation for this situation would be:
dy
y(0) =
A tank contains 60 kg of salt and 1000 L of water. A solution of a concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min. The solution is mixed and drains from the tank at the same rate.
Let y be the number of kg of salt in the tank after t minutes.
Write the differential equation for this situation
dy =
y(0) = 60
y' + ty^1/3 = tan(t), y(3) = – 5
a) Rewrite the differential equation, if necessary, to obtain the form y' = f(t, y)
F(t, x) = _______
b) Compute the partial derivative of f with respect to y. Determine where in the ty-plane both f(t, y) and its derivative are continuous.
c) Find the largest open rectangle in the ty-plane on which the solution of the initial value problem above is certain to exist for the initial condition. (Enter oo for infinity)
t interval is
y interval is