Explanation Procedure used: The solution to a differential equation using Euler’s method. Consider the general iteration formula of Euler’s y n = y n − 1 + h f ( x n − 1 , y n − 1 ) where h is the step size and f is the function given in the form d y d x = f ( x , y ) . From the general iteration formula of Euler’s the value of y 1 can be obtained as y 1 = y o + h f ( x o , y o ) , similarly the value of y 2 , y 3 y 4 ,…, y n can be found. Then, substitute the given values of x o and y o in the Euler’s equation to obtain the values of y 1 similarly find the value of y 2 . Calculation: Simplify the differential equation y ′ = 2 x − 3 y + 1 . y ′ = 2 x − 3 y + 1 d y d x = 2 x − 3 y + 1 Here, the function is 2 x − 3 y + 1 . Calculate the value of y 1 by substituting 0.1 for h , 1 for x o , and 5 for y o in the iteration formula of Euler’s formula. y 1 = 5 + 0.1 f ( 1 , 5 ) = 5 + 0.1 [ 2 ( 1 ) − 3 ( 5 ) + 1 ] = 3.8 Calculate the value of y 2 by substituting 0.1 for h , 1.1 for x 1 and 3.8 for y 1 in the iteration formula of Euler’s formula. y 2 = 3.8 + 0.1 f ( 1.1 , 3.8 ) = 3

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ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.6, Problem 1E

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The solution of the differential equation y′=2x−3y+1 using Euler’s method where y(1)=5 with step size h=0.1 and h=0.05.

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Chapter 2.5, Problem 37E

Chapter 2.6, Problem 2E

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The solution of the differential equation y ′ = 2 x − 3 y + 1 using Euler’s method where y ( 1 ) = 5 with step size h = 0.1 and h = 0.05 .

Solution Summary: The author explains how to solve the differential equation yprime using Euler's method.

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The solution of the differential equation y′=2x−3y+1 using Euler’s method where y(1)=5 with step size h=0.1 and h=0.05.

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Chapter 2 Solutions