#1.) Given the differential equation, y'=4cosx- 3y, y(0)=1, a.) Use Euler's Method to approximate the value of y(0.5) using h=0.5 b.) Use Euler's Method to approximate the value of y(0.5) using h=0.1 c.) Use Euler's Method to approximate the value of y(0.5) using h=0.05
#1.) Given the differential equation, y'=4cosx- 3y, y(0)=1, a.) Use Euler's Method to approximate the value of y(0.5) using h=0.5 b.) Use Euler's Method to approximate the value of y(0.5) using h=0.1 c.) Use Euler's Method to approximate the value of y(0.5) using h=0.05
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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Transcribed Image Text:#1.) Given the differential equation, y'=4cosx-3y, y(0)=1,
a.) Use Euler's Method to approximate the value of y(0.5) using h=0.5
b.) Use Euler's Method to approximate the value of y(0.5) using h=0.1
c.) Use Euler's Method to approximate the value of y(0.5) using h=0.05
Please provide the following columns: n, Xn, Yn, Ynt1
# 2.) Given the differential equation, y'=4cos x-3 y, y(0)=1,
|
a.) Use Euler's Improved Method to approximate the value of y(0.5) using h=0.5
b.) Use Euler's Improved Method to approximate the value of y(0.5) using h=0.1
c.) Use Euler's Improved Method to approximate the value of y(0.5) using h=0.05
Please provide the following columns: n, Xn, Yn: Yt> M1, M2, M, yn+1
y'= 4cosx-3y, y(0)=1,
# 3.) Given the differential equation,
a.) Use R-K, 4th-Order Method to approximate the value of y(0.5) using h= 0.5
b.) Use R-K, 4th-Order Method to approximate the value of y(0.5) using h=0.1
c.) Use R-K, 4th-Order Method to approximate the value of y(0.5) using h=0.05
%3D
%3D
Please provide the following columns: n, Xn, Yn; M1, M2, M2, M4, M, yn+1
# 4.) Given the differential equation, y'=4 cos x-3y, y(0)=1,
a.) Solve using methods discussed earlier in the course ( Linear, First Order ).
b.) Use your solution from # 4a to find y(0.5).
This value will be used as the exact value for your Error Analysis in Problem #4c.
c.) Create a table as shown on the template provided so I can see the results of your
problems, #1 – #3.
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