Explanation Given: The differential function and initial value is given as, d y d x = x + y − 1 f ( x , y ) = x + y − 1 ... ( 1 ) y ( 0 ) = 1 ; h = 0 .2 . Approach: The value of x i + 1 = x i + h . y i + 1 = y i + h f ( x i , y i ) ... ( 2 ) Calculation: The value of y ( 1 ) is calculated as, The value of x 0 , y 0 put up in the equation ( 1 ) . f ( x 0 , y 0 ) = 0 + 1 − 1 ; y ( 0 ) = 1 f ( x 0 , y 0 ) = 1 The values of x 0 , y 0 put up in the equation ( 2 ) . y 1 = y 0 + h f ( x 0 , y 0 ) y 1 = 1 + 0.2 ⋅ 1 y 1 = 1.2 From x i + 1 = x i + h ; x 1 = x 0 + h ; x 1 = 0.2 The values of x 1 , y 1 put up in the equation ( 2 ) . y 2 = y 1 + h f ( x 1 , y 1 ) y 2 = 1.2 + 0.2 f ( 0.2 , 1.2 ) y 2 = 1.2 + 0.2 ( 0.2 + 1.2 − 1 ) y 2 = 1

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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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 11.CR, Problem 48CR

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Using Euler’s method approximation, determine the value of y(1) for the function dydx=x+y−1.

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Chapter 11.CR, Problem 47CR

Chapter 11.CR, Problem 49CR

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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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Using Euler’s method approximation, determine the value of y ( 1 ) for the function d y d x = x + y − 1 .

Solution Summary: The author calculates the value of y(1) using Euler’s method approximation.

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To find:

Using Euler’s method approximation, determine the value of y(1) for the function dydx=x+y−1.

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Chapter 11 Solutions

Using Euler’s method approximation, determine the value of y ( 1 ) for the function d y d x = x + y − 1 .

Solution Summary: The author calculates the value of y(1) using Euler’s method approximation.

Concept explainers

Videos

To find: Using Euler’s method approximation, determine the value of y(1) for the function dydx=x+y−1.

Want to see the full answer?

Chapter 11 Solutions

To find:

Using Euler’s method approximation, determine the value of y(1) for the function dydx=x+y−1.