Program Explanation Given information: The differential equation is y ′ = y + 1 and the function is y ( x ) = C e x − 1 and initialcondition is y ( 0 ) = 5 . Calculation: Label the given function as, y ( x ) = C e x − 1 ........ (1) Label and rewrite the given differential function as, y ′ − y − 1 = 0 ........ (2) Label the given initial condition as, y ( 0 ) = 5 ........ (3) Differentiate equation (1) with respect to x as shown below. y ′ ( x ) = d d x ( C e x − 1 ) = C e x − 0 = C e x Substitute C e x for y ′ and C e x − 1 for y in the left hand side ( L .H .S ) of theequation (2) as, L .H .S = C e x − ( C e x − 1 ) − 1 = C e x − C e x + 1 − 1 = 0 The right hand side ( R

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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 1.1, Problem 19P

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 18P

Chapter 1.1, Problem 20P

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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