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wksht03 - MATH 152 L1 L2 Applied Linear Algebra and...

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MATH 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 03 Worksheet (February 14, 2005) : First-Order Differential Equations Q1. (Existence and uniqueness for nonlinear equations) Consider the differential equation y 0 = ( y - 5) 1 3 . (a) Find the equilibrium (i.e., constant) solution(s). (b) Use the fact that the equation is separable to find a nonconstant solution satisfying the initial condition y (1) = 5. (c) Explain why Theorem 2.4.2 (page 27) does not apply to say there is a unique solution. Q2. (Modeling) A drug is injected into a patient’s bloodstream at a constant rate 0 . 01 g/s. If the drug diffuses out of the bloodstream at a rate proportional to the amount of drug q ( t ) present at any instant with rate constant k , find an expression for the amount of drug present in the bloodstream at any time. Q3. (Newton’s Cooling Law) The temperature of a house drop from 25 C to 20 C in 40 minutes when the outside temperature is - 5 C. By Newton’s Law of Cooling, the rate of decrease of the temperature
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