Math 213
Name:
Quiz 4
1. [12 points] Water is being drained from the bottom of an inverted conical tank. According to
Torricelli’s law, the volume V of the water left in the tank obeys the differential equation
dV
= −kV 1/3
dt
where k is a constant.
(a) [4 pts] Find the general solution to the above equation.
(b) [8 pts] Suppose the tank holds 1000 L of water, and that water initially drains from the tank at
a rate of 0.20 L/sec. How long will it take for the tank to drain completely?
2. [5 points] Consider the following initial-value problem
y0 = x + y2 − 3.6,
y(0) = 2.
Use Euler’s method with step size ∆x = 0.5 to estimate y(1).
3. [3 points] Which of the following graphs shows a solution to the equation y0 = x2 − y2 ?
(Circle your answer.)