Program Explanation Given information: The differential equation is d y d x = x 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, which is done 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 . Separate the variables of the above differential equation as, d y = x d x Now integrate the equation on both the sides. ∫ d y = ∫ x d x Now evaluate the above integral as, y = 2 3 ( x ) 3 2 + C ........ (1) Therefore, the general equation of the given differential equation is y = 2 3 ( x ) 3 2 + C

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. 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 3P

Program Plan Intro

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

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Chapter 1.2, Problem 2P

Chapter 1.2, Problem 4P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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The particular function y = f ( x ) that satisfy the differential equation d y d x = x and the initial condition is y ( 4 ) = 0 .

Solution Summary: The author explains how the differential equation dy=sqrtx can be calculated with the help of separating the variables.

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

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Chapter 1 Solutions