Program Explanation Given information: The differential equation is x y ′ − 3 y = x 3 and the function is y ( x ) = x 3 ( C + ln x ) and initialcondition is y ( 1 ) = 17 . Calculation: Label the given function as, y ( x ) = x 3 ( C + ln x ) ........ (1) Label and rewrite the given differential function as, x y ′ − 3 y − x 3 = 0 ........ (2) Label the given initial condition as, y ( 1 ) = 17 ........ (3) Differentiate equation (1) with respect to x as shown below. y ′ ( x ) = d d x ( x 3 ( C + ln x ) ) = 3 x 2 ( C + ln x ) + x 3 ⋅ 1 x = 3 x 2 ( C + ln x ) + x 2 Substitute 3 x 2 ( C + ln x ) + x 2 for y ′ and x 3 ( C + ln x ) for y in the left hand side ( L .H .S ) of theequation (2) as, L .H

5th Edition

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.

Question

Chapter 1.1, Problem 24P

Program Plan Intro

To find: The value of the constant C such that y(x) satisfies the given initial condition and also sketch the solution of the given differential equation.

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Chapter 1.1, Problem 23P

Chapter 1.1, Problem 25P

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Chapter 1 Solutions

DIFFERENTIAL EQUATIONS+..-MYLAB ACCESS

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The value of the constant C such that y ( x ) satisfies the given initial condition and also sketch the solution of the given differential equation.

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To find: The value of the constant C such that y(x) satisfies the given initial condition and also sketch the solution of the given differential equation.

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Chapter 1 Solutions