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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?