Program Explanation Given information: The differential equation is d y d x = x x 2 + 9 and initial condition is y ( − 4 ) = 0 . Concept used: The differential equation d y d x = f ( x ) g ( y ) can be calculated with the help of separating the variables as, ∫ d y g ( y ) = ∫ f ( x ) d x The integral of the function x n can be calculated as, ∫ x n d x = x n + 1 n + 1 + c Here, c is called the constant of integration. Calculation: The given differential equation is d y d x = x x 2 + 9 . Separate the variables of the above differential equation as, d y = x x 2 + 9 d x Now take t for x 2 + 9 and then differentiate with respect to x as, t = x 2 + 9 d t d x = 2 x d x = d t 2 x Now integrate the equation on both the sides. ∫ d y = ∫ x x 2 + 9 d x ........ (1) Now substitute t for x 2 + 9 and d x for d t 2 x in equation (1). ∫ d y = ∫ x t d t 2 x Now evaluate the above integral as, ∫ d y = 1 2 ∫ t d t y = 1 2 ⋅ 2 3 ( t ) 3 2 + C y = 1 3 ( t ) 3 2 + C Now substitute x 2 + 9 for t in the resultant equation

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

Author: Edwards, C., Penney, David, Calvis

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 1.2, Problem 6P

Program Plan Intro

To find: A particular function y=f(x) that satisfy the differential equation dydx=xx2+9 and the initial condition is y(−4)=0 .

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Chapter 1.2, Problem 5P

Chapter 1.2, Problem 7P

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Chapter 1 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

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A particular function y = f ( x ) that satisfy the differential equation d y d x = x x 2 + 9 and the initial condition is y ( − 4 ) = 0 .

Solution Summary: The author explains how the differential equation dysqrtx2+9 can be calculated with the help of separating the variables.

Concept explainers

To find: A particular function y=f(x) that satisfy the differential equation dydx=xx2+9 and the initial condition is y(−4)=0 .

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Chapter 1 Solutions