Program Explanation Given information: The differential equation is d y d x = 10 x 2 + 1 and initial condition is y ( 0 ) = 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 1 x 2 + 1 can be calculated as, ∫ 1 x 2 + 1 d x = tan − 1 x + C Here, C is the constant of integration. Calculation: The given differential equation is d y d x = 10 x 2 + 1 . Separate the variables of the above differential equation as, d y = 10 x 2 + 1 d x Now integrate the equation on both the sides. ∫ d y = ∫ 10 x 2 + 1 d x

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 1.2, Problem 7P

Program Plan Intro

To find: A particular function y=f(x) that satisfy the differential equation dydx=10x2+1 and the initial condition is y(0)=0 .

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Chapter 1.2, Problem 6P

Chapter 1.2, Problem 8P

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Chapter 1 Solutions

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A particular function y = f ( x ) that satisfy the differential equation d y d x = 10 x 2 + 1 and the initial condition is y ( 0 ) = 0 .

Solution Summary: The author explains how the differential equation can be calculated by separating the variables and integrating the equation on both sides.

Concept explainers

To find: A particular function y=f(x) that satisfy the differential equation dydx=10x2+1 and the initial condition is y(0)=0 .

Want to see the full answer?

Chapter 1 Solutions