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Unformatted text preview: Homework 1 (25 points) Due date: September 16th, 2009 I will only grade 3 problems at random. & 1 : Solve the given initial-value problem: y dy dx = & y 3 1 e ax 2 x y ; y (0) = 1 ; where a > is a &xed constant. & 2 : Consider the initial-value problem: y + 2 3 y = 1 1 2 x; y (0) = y : Find the value of y for which the solution touches, but does not cross, the x-axis (you may use a calculator!). & 3 : Newtons emperical law of cooling/warming of an object is given by the linear &rst order dierential equations d T dt = k ( T T ambient ) ; (*) where k is a constant of proportionality, t is time, T ( t ) is the temperature for the object for t > and T ambient is the ambient temperature, that is, the temperature of the medium around the object. In general, T ambient is assumed to be constant. Problem: In &xing time of death, coroners use a formulation based on Newtons law of cooling ( ) . This law states that the rate of change in the temperature T ( t ) of a body in this case is directly proportional to the dierence between the temperature of...
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