To determine The approximate value of y ( 0.5 ) up to 3 decimal places by Euler’s method for differential equation d y d x = x 2 + y 2 . Explanation Given: The differential equation is d y d x = x 2 + y 2 , the initial value is y ( 0 ) = 2 and step size is h = 0.1 . Formula used: Euler’s method: As per the Euler’s method the solution of a linear differential equation of the form y ′ = f ( x , y ) is given as follows: y n + 1 = y n + h f ( x n , y n ) Calculation: The linear differential equation is given as follows: y ′ = x 2 + y 2 The initial value is given as y ( 0 ) = 2 . This implies that x 0 = 0 and y 0 = 2 . The given differential equation is of the form y ′ = f ( x ) . f ( x , y ) = x 2 + y 2 Obtain the solution of the given differential equation by Euler’s method for h = 0.1 . The solution of a linear differential equation of the form y ′ = f ( x , y ) by the Euler’s method is given as follows: y n + 1 = y n + h f ( x n , y n ) … … ( 1 ) Substitute 0 for n in equation ( 1 ) to obtain the equation of y 1 as shown below

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Differential Equations

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Chapter 10.3, Problem 1E

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The approximate value of y(0.5) up to 3 decimal places by Euler’s method for differential equation dydx=x2+y2.

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Chapter 10.3, Problem 1YT

Chapter 10.3, Problem 2E

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Calculus with Applications (11th Edition)

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

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