Program Explanation Given information: The differential equation is written as, d y d x = 4 x ( y + 2 x 2 ) The initial value for the above differential equation is written as, y ( 0 ) = 0 Calculation: Substitute 4 x ( y + 2 x 2 ) for f ( x , y ) , 0 for a and 0 for b in the iteration formula as, y n + 1 ( x ) = b + ∫ a x f ( t , y n ( t ) ) d t y 1 ( x ) = 0 + ∫ 0 x f ( t , y 0 ( t ) ) d t y 1 ( x ) = ∫ 0 x 4 t ( 0 + 2 t 2 ) d t y 1 ( x ) = 2 x 4 Now obtain the second iteration from the use of above calculation as, y 2 ( x ) = 0 + ∫ 0 x f ( t , y 1 ( t ) ) d t y 2 ( x ) = ∫ 0 x 4 t ( 2 t 4 + 2 t 2 ) d t y 2 ( x ) = ∫ 0 x ( 8 t 5 + 8 t 3 ) d t y 2 ( x ) = 4 x 6 3 + 2 x 4 Do similar process for the third iteration from the use of above calculation as, y 3 ( x ) = 0 + ∫ 0 x f ( t , y 2 ( t ) ) d t y 3 ( x ) = ∫ 0 x 4 t ( 4 t 6 3 + 2 t 4 + 2 t 2 ) d t y 3 ( x ) = ∫ 0 x ( 16 t 7 3 + 8 t 5 + 8 t 3 ) d t y 3 ( x ) = 2 x 8 3 + 4 x 6 3 + 2 x 4 Similarly, for the fourth iteration from the use of above calculation as, y 4 ( x ) = 0 + ∫ 0 x f ( t , y 3 ( t ) ) d t y 4 ( x ) = ∫ 0 x 4 t ( 2 t 8 3 + 4 t 6 3 + 2 t 4 + 2 t 2 ) d t y 4 ( x ) = ∫ 0 x

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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Chapter A.5, Problem 8P

Program Plan Intro

Program Description: Purpose of the problem is to solve initial value problem dydx=4x(y+2x2),y(0)=0 to compute yn(x) for n≤4 and then write the solution in exponential series.

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Chapter A.5, Problem 7P

Chapter A.5, Problem 9P

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Chapter A Solutions

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

Ch. A.5 - In Problems 1 through 8, compute the successive...Ch. A.5 - Prob. 2P Ch. A.5 - Prob. 3P Ch. A.5 - Prob. 4P Ch. A.5 - Prob. 5P Ch. A.5 - Prob. 6P Ch. A.5 - Prob. 7P Ch. A.5 - Prob. 8P Ch. A.5 - Prob. 9P Ch. A.5 - Prob. 10P

Ch. A.5 - Prob. 11P Ch. A.5 - Prob. 12P Ch. A.5 - Prob. 13P Ch. A.5 - Prob. 14P Ch. A.5 - Prob. 15P Ch. A.5 - Prob. 16P Ch. A.5 - Prob. 17P Ch. A.5 - Prob. 18P

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Program Description: Purpose of the problem is to solve initial value problem d y d x = 4 x ( y + 2 x 2 ) , y ( 0 ) = 0 to compute y n ( x ) for n ≤ 4 and then write the solution in exponential series.

Solution Summary: The author explains the purpose of the problem, which is to solve the initial value problem y(y+2x2 ) and then write the solution in exponential series.

Program Description: Purpose of the problem is to solve initial value problem dydx=4x(y+2x2),y(0)=0 to compute yn(x) for n≤4 and then write the solution in exponential series.

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Chapter A Solutions