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 ???
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff585c19b-ef83-4b9a-93dd-0cb9fc8d5f5b%2F7e63db72-8227-41e0-8001-eb2fc58ee6b0%2Fnymh6eb_processed.png&w=3840&q=75)
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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