Program Explanation Given information: Substitute u for v ρ / g . Explanation: From the given information, separate variables as follows: d v d t = − g + ρ v 2 d v g − ρ v 2 = − d t 1 g d v 1 − ρ g v 2 = − d t d v 1 − ρ g v 2 = − g d t Further, solve the differential equation as, ∫ d v 1 − ρ g v 2 = − g ∫ d t g ρ ∫ d u 1 − u 2 = − g ∫ d t ∫ d u 1 − u 2 = − ρ g ∫ d t tanh − 1 ( u ) = C 2 − t ρ g Further solve the above differential equation as, tanh − 1 <

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ISBN: 9780135904206

Author: Edwards

Publisher: PEARSON

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

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Chapter 2.3, Problem 15P

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Program Description: Purpose of the problem is to obtain the downward velocity function v(t)=gρtanh(C2−tρg) where C2=tanh−1(v0ρg) with initial condition v(0)=v0 from dvdt=−g+ρv2 .

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Chapter 2.3, Problem 14P

Chapter 2.3, Problem 16P

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DIFFERENTIAL EQUATIONS+..-MYLAB ACCESS

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Program Description: Purpose of the problem is to obtain the downward velocity function v ( t ) = g ρ tanh ( C 2 − t ρ g ) where C 2 = tanh − 1 ( v 0 ρ g ) with initial condition v ( 0 ) = v 0 from d v d t = − g + ρ v 2 .

Solution Summary: The author explains that the problem is to obtain the downward velocity function v(t)=sqrt

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Program Description: Purpose of the problem is to obtain the downward velocity function v(t)=gρtanh(C2−tρg) where C2=tanh−1(v0ρg) with initial condition v(0)=v0 from dvdt=−g+ρv2 .

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Chapter 2 Solutions