Program Explanation Given information: The differential equation is x 3 y ′ = x 2 y − y 3 . Explanation: The given differential equation can be written as, d y d x = x 2 y − y 3 x 3 = y x − y 3 x 3 The above equation is a homogeneous equation. Consider v = y x and differentiate with respect to x . d d x ( v x ) = d y d x v + x d v d x = d y d x The given differential equation can be written as, v + x d v d x = v − v 3 x d v d x = − v 3 d v v 3 = − d x x Integrate both sides of above equation. ∫ v − 3 d v = − ln x + C v − 2 − 2 = − ln x + C − 1 2 v 2 = ln x + C Simplify the above equation

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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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 1, Problem 14RP

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Program Description: Purpose of problem is to calculate the general solution of the differential equation x3y′=x2y−y3 .

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Chapter 1, Problem 13RP

Chapter 1, Problem 15RP

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2. (5 points) Let f(x) = = - - - x² − 3x+7. Find the local minimum and maximum point(s) of f(x), and write them in the form (a, b), specifying whether each point is a minimum or maximum. Coordinates should be kept in fractions. Additionally, provide in your answer if f(x) has an absolute minimum or maximum over its entire domain with their corresponding values. Otherwise, state that there is no absolute maximum or minimum. As a reminder, ∞ and -∞ are not considered absolute maxima and minima respectively.

Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Program Description: Purpose of problem is to calculate the general solution of the differential equation x 3 y ′ = x 2 y − y 3 .

Solution Summary: The author explains that the differential equation is a homogeneous equation.

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Program Description: Purpose of problem is to calculate the general solution of the differential equation x3y′=x2y−y3 .

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Chapter 1 Solutions