Explanation Given: The given condition is: d y d x = y 2 ; y ( 0 ) = 1 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 And, General solution of d y d x = p ( x ) q ( y ) : ∫ q ( y ) d y = ∫ p ( x ) d x Calculation: Consider the given differential equation: d y d x = y 2 ; y ( 0 ) = 1 We can write as: g ( x , y ) = y 2 Substitute the value 0 for x and 1 for y : g ( x 0 , y 0 ) = ( 1 ) 2 = 1 and, y 1 = y 0 + g ( x 0 , y 0 ) h = 1 + 1 ( 0 To determine (b) To solve: The given equation using separation of variable. To determine (c) To explain: The reasons for Euler’s method to be wrong.

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

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Chapter 11.3, Problem 31E

To determine

(a)

To find:

The approximate value of f(1) with h=0.2 for the given condition.

To determine

(b)

To solve:

The given equation using separation of variable.

To determine

(c)

To explain:

The reasons for Euler’s method to be wrong.

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Chapter 11.3, Problem 29E

Chapter 11.3, Problem 33E

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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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(a) To find: The approximate value of f ( 1 ) with h = 0.2 for the given condition.

Solution Summary: The author explains how to find the approximate value of f(1) with h=0.2 for the given condition.

Concept explainers

Videos

(a)

To find:

The approximate value of f(1) with h=0.2 for the given condition.

(b)

To solve:

The given equation using separation of variable.

(c)

To explain:

The reasons for Euler’s method to be wrong.

Want to see the full answer?

Chapter 11 Solutions

(a) To find: The approximate value of f ( 1 ) with h = 0.2 for the given condition.

Solution Summary: The author explains how to find the approximate value of f(1) with h=0.2 for the given condition.

Concept explainers

Videos

(a) To find: The approximate value of f(1) with h=0.2 for the given condition.

(b) To solve: The given equation using separation of variable.

(c) To explain: The reasons for Euler’s method to be wrong.

Want to see the full answer?

Chapter 11 Solutions

(a)

To find:

The approximate value of f(1) with h=0.2 for the given condition.

(b)

To solve:

The given equation using separation of variable.

(c)

To explain:

The reasons for Euler’s method to be wrong.