Explanation Given: The given differential equation is: d y d x − 2 y = e 2 x ; y ( 0 ) = 10 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 − 2 y = e 2 x ; y ( 0 ) = 10 We can write as: g ( x , y ) = e 2 x + 2 y Substitute the value 0 for x and 10 for y : g ( x 0 , y 0 ) = e 2 ( 0 ) + 2 ( 10 ) = 21 and, y 1 = y 0 + g ( x 0 , y 0 ) h = 10 + 21 ( 0.1 ) = 12.1 Now, x 1 = 0.1 , y 1 = 12

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 20E

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The value of y(0.4) for the given differential equation by using Euler’s method and by indicating function value.

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Chapter 11.3, Problem 19E

Chapter 11.3, Problem 21E

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The value of y ( 0.4 ) for the given differential equation by using Euler’s method and by indicating function value.

Solution Summary: The author calculates the value of y(0.4) for the given differential equation by using Euler's method and by indicating function value.

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To find:

The value of y(0.4) for the given differential equation by using Euler’s method and by indicating function value.

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Chapter 11 Solutions

The value of y ( 0.4 ) for the given differential equation by using Euler’s method and by indicating function value.

Solution Summary: The author calculates the value of y(0.4) for the given differential equation by using Euler's method and by indicating function value.

Concept explainers

Videos

To find: The value of y(0.4) for the given differential equation by using Euler’s method and by indicating function value.

Want to see the full answer?

Chapter 11 Solutions

To find:

The value of y(0.4) for the given differential equation by using Euler’s method and by indicating function value.