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Math 213
Name:
Quiz 3
1. [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).
2. [3 points] In a certain electrical circuit with an inductor and a resistor, the electric current I obeys
the equation
dI
= −kI,
dt
where k = 0.12/sec. Assuming the initial current in the circuit is 1.5 amps, how much current will
there be after 2.0 seconds?
3. [12 points] When a hospital patient is administered morphine intravenously, the volume V of morphine in the bloodstream obeys the equation
dV
= r − kV
dt
where r is the flow rate of the morphine, and k = 0.35/hour.
(a) Find the general solution to the above equation.
(b) A patient is connected to an IV drip that administers morphine at a rate of 1.5 mg/hour. How
much morphine will there be in the patient’s bloodstream after 1 hour?