Program Explanation Given information: The differential equation is y 3 d y d x = ( y 4 + 1 ) cos x . Concept used: The differential equation d y d x = f ( x ) g ( y ) can be calculated with the help of separating the variables, which is done as, ∫ d y g ( y ) = ∫ f ( x ) d x Calculation: The given differential equation is y 3 d y d x = ( y 4 + 1 ) cos x . Separate the variables of the above differential equation as, y 3 d y ( 1 + y 4 ) = cos x d x Now, integrate the equation on both the sides. ∫ y 3 d y ( 1 + y 4 ) = ∫ cos x d x ....... (1) Suppose u = 1 + y 4 . Differentiate u = 1 + y 4 with respect to x as, d u d x = 0 + 4 y 3 d y d x d u = 4 y 3 d y d u 4 y 3 = d y Substitute u for 1 + y 4 and d u 4 y 3 for d y in equation (1) to obtain the value of y as,

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.

Question

Chapter 1.4, Problem 13P

Program Plan Intro

To find: A general solution of the differential equation y3dydx=(y4+1)cosx .

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Chapter 1.4, Problem 12P

Chapter 1.4, Problem 14P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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A general solution of the differential equation y 3 d y d x = ( y 4 + 1 ) cos x .

Solution Summary: The author explains how the differential equation can be solved with the help of separating the variables.

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To find: A general solution of the differential equation y3dydx=(y4+1)cosx .

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Chapter 1 Solutions