Explanation Approach: Let y = f ( x ) be the solution of the differential equation: d y d x = g ( x , y ) , with y ( x 0 ) = y 0 For x 0 ≤ x ≤ x n , let x i + 1 = x i + h , where h = ( x n − x 0 ) n and, y i + 1 = y i + g ( x i , y i ) h For 0 ≤ i ≤ n − 1 . Then, f ( x i + 1 ) ≈ y i + 1 Calculation: Consider the given differential equation: d y d x = x 2 + y 2 ; y ( 0 ) = 2 We can write as: g ( x , y ) = x 2 + y 2 Substitute the value 0 for x and 2 for y : g ( x 0 , y 0 ) = ( 0 ) 2 + ( 2 ) 2 = 4 and, y 1 = y 0 + g ( x 0 , y 0 ) h = 2 + 4 ( 0.1 ) = 2

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 11.3, Problem 1E

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The value of y(0.5) for the given differential equation dydx=x2+y2; y(0)=2.

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Chapter 11.3, Problem 1YT

Chapter 11.3, Problem 2E

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Chapter 11 Solutions

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 11.1 - YOUR TURN 1 Find all solutions of the differential...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - YOUR TURN In Example 6, find the goat population...Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 2E Ch. 11.1 - Find the general solution for each differential...Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E

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The value of y ( 0.5 ) for the given differential equation d y d x = x 2 + y 2 ; y ( 0 ) = 2 .

Solution Summary: The author explains that the value of y(0.5) for the given differential equation is 8.273.

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To find:

The value of y(0.5) for the given differential equation dydx=x2+y2; y(0)=2.

Want to see the full answer?

Chapter 11 Solutions

The value of y ( 0.5 ) for the given differential equation d y d x = x 2 + y 2 ; y ( 0 ) = 2 .

Solution Summary: The author explains that the value of y(0.5) for the given differential equation is 8.273.

Videos

To find: The value of y(0.5) for the given differential equation dydx=x2+y2; y(0)=2.

Want to see the full answer?

Chapter 11 Solutions

To find:

The value of y(0.5) for the given differential equation dydx=x2+y2; y(0)=2.