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1. Consider the ODE Numerical Methods for Solving ODE Euler Method ylny dx - xdy = 0 With initial condition: y(2) = e a. Determine the general solution using appropriate analytical process. Find the particular solution using the given initial condition. b. c. Using Euler method, approximate the solution at x = 3.0 using a step size h = 0.1 y ???

1. Consider the ODE Numerical Methods for Solving ODE Euler Method ylny dx - xdy = 0 With initial condition: y(2) = e a. Determine the general solution using appropriate analytical process. Find the particular solution using the given initial condition. b. c. Using Euler method, approximate the solution at x = 3.0 using a step size h = 0.1 y ???

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the ODE Numerical Methods for Solving ODE Euler Method ylny dx - xdy = 0 With initial condition: y(2) = e a. Determine the general solution using appropriate analytical process. Find the particular solution using the given initial condition. b. c. Using Euler method, approximate the solution at x = 3.0 using a step size h = 0.1 y ??? d. What is the relative absolute error at x = 3.0 using a step size h = 0.1? %Errabs = ??? e. Repeat (c) and (d) using a step size h = 0.05. f. Repeat (c) and (d) using a step size h = 0.025. g. What can you conclude from the results in (d), (e) and (f)? Show sample of computation below (and attach soft copy of Excel computation).
Transcribed Image Text:1. Consider the ODE Numerical Methods for Solving ODE Euler Method ylny dx - xdy = 0 With initial condition: y(2) = e a. Determine the general solution using appropriate analytical process. Find the particular solution using the given initial condition. b. c. Using Euler method, approximate the solution at x = 3.0 using a step size h = 0.1 y ??? d. What is the relative absolute error at x = 3.0 using a step size h = 0.1? %Errabs = ??? e. Repeat (c) and (d) using a step size h = 0.05. f. Repeat (c) and (d) using a step size h = 0.025. g. What can you conclude from the results in (d), (e) and (f)? Show sample of computation below (and attach soft copy of Excel computation).
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