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Consider the following first-order ODE: dy =y+x³ from x = 0.5 to x = 2.1 1with y(0.5) = -1 dx Solve using Euler's explicit method. (h= 0.4) 71e* The analytical solution of the ODE is: y=-x³-3x2 - 6x-6+; In each part, calculate the error between the true solution 8e0.5 and the numerical solution at the points where the numerical solution is determined.

Consider the following first-order ODE: dy =y+x³ from x = 0.5 to x = 2.1 1with y(0.5) = -1 dx Solve using Euler's explicit method. (h= 0.4) 71e* The analytical solution of the ODE is: y=-x³-3x2 - 6x-6+; In each part, calculate the error between the true solution 8e0.5 and the numerical solution at the points where the numerical solution is determined.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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Consider the following first-order ODE: dy dx =y+x³ from x = 0.5 to x = 2.1 1with y(0.5) = -1 Solve using Euler's explicit method. (h= 0.4) 71e* The analytical solution of the ODE is: y=-x³-3x² - 6x-6+ 8e0.5 and the numerical solution at the points where the numerical solution is determined. X 0.5 0.9 1.3 y -1 -1.35 -1.6 error 0 0.0309 0.2831 X 0.5 0.9 1.3 y -1 -1.33 -1.38 error 0 0.0137 0.0665 X 0.5 0.9 1.3 y -1 -1.32 -1.32 error 0 0 0.0002 None of the choices In each part, calculate the error between the true solution 1.7 -1.36 1.042 1.7 -0.52 0.2024 1.7 -0.32 0.0008 2.1 0.0 2.8 2.1 2.3 0.4 2.1 2.8 0.0
Transcribed Image Text:Consider the following first-order ODE: dy dx =y+x³ from x = 0.5 to x = 2.1 1with y(0.5) = -1 Solve using Euler's explicit method. (h= 0.4) 71e* The analytical solution of the ODE is: y=-x³-3x² - 6x-6+ 8e0.5 and the numerical solution at the points where the numerical solution is determined. X 0.5 0.9 1.3 y -1 -1.35 -1.6 error 0 0.0309 0.2831 X 0.5 0.9 1.3 y -1 -1.33 -1.38 error 0 0.0137 0.0665 X 0.5 0.9 1.3 y -1 -1.32 -1.32 error 0 0 0.0002 None of the choices In each part, calculate the error between the true solution 1.7 -1.36 1.042 1.7 -0.52 0.2024 1.7 -0.32 0.0008 2.1 0.0 2.8 2.1 2.3 0.4 2.1 2.8 0.0
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