Program Explanation Given information: The differential equation is d y d x = 3 x 2 ( y 2 + 1 ) and initial condition is y ( 0 ) = 1 . Concept used: The differential equation is 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 Calculation: The given differential equation is d y d x = 3 x 2 ( y 2 + 1 ) . Separate the variables of the above differential equation as, d y y 2 + 1 = 3 x 2 d x Now integrate the equation on both the sides as, ∫ d y y 2 + 1 = ∫ 3 x 2 d x tan − 1 y = 3 x 3 3 + C tan − 1 y = x 3 + C y = tan ( x 3 + C ) Here, C is the constant of integration. Therefore, the general equation of the differential equation d y d x = 3 x 2 ( y 2 + 1 ) is y = tan ( x 3 + 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.

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Chapter 1.4, Problem 20P

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To find: The particular solution of the initial value problem dydx=3x2(y2+1) and the initial conditionis y(0)=1 .

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Chapter 1.4, Problem 19P

Chapter 1.4, Problem 21P

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Chapter 1 Solutions

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

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The particular solution of the initial value problem d y d x = 3 x 2 ( y 2 + 1 ) and the initial conditionis y ( 0 ) = 1 .

Solution Summary: The author explains how the differential equation can be calculated with the help of separating the variables as cdisplaystyle

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To find: The particular solution of the initial value problem dydx=3x2(y2+1) and the initial conditionis y(0)=1 .

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Chapter 1 Solutions