Explanation Given: d z d x + g ( x ) z 2 = f ( x ) where f ( x ) = 5 x + 2 and g ( x ) = x 2 which implies d z d x = 5 x − x 2 z 2 + 2 ∈ = 0.0001 . Approach: The recursive formulas for Runge-Kutta method are x n + 1 = x n + h , z n + 1 = z n + 1 6 ( k 1 + 2 k 2 + 2 k 3 + k 4 ) , Where k 1 = h f ( x n + z n ) , k 2 = h f ( x n + h 2 , z n + k 1 2 ) , k 3 = h f ( x n + h 2 , z n + k 2 2 ) , k 4 = h f ( x n + h , z n + k 3 ) Calculation: Consider, k = z 0 = 1 The inputs are z 0 = 1 , x 0 = 0 , c = 1 f ( x , z ) = 5 x − x 2 z 2 + 2 The initial value for N in this algorithm is N = 1 , so h = ( c − x 0 N ) = ( 1 − 0 1 ) = 1 ∴ k 1 = h f ( x 0 , z 0 ) = 1 f ( 0 , 1 ) = 2 ,

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ISBN: 9780321977175

Author: Nagle

Publisher: PEARSON CO

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 3.7, Problem 21E

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The solution of the given initial value problem at x=1.

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Chapter 3.7, Problem 20E

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EBK FUND.OF DIFF.EQUATIONS+BOUNDARY...

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To approximate: The solution of the given initial value problem at x = 1 .

Solution Summary: The author approximates the solution of the given initial value problem at x=1 by using Runge-Kutta method.

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The solution of the given initial value problem at x=1.

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To approximate: The solution of the given initial value problem at x = 1 .

Solution Summary: The author approximates the solution of the given initial value problem at x=1 by using Runge-Kutta method.

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To approximate: The solution of the given initial value problem at x=1.

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Chapter 3 Solutions

To approximate:

The solution of the given initial value problem at x=1.