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# 4.) Given the differential equation, y'=4cosx-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

# 4.) Given the differential equation, y'=4cosx-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

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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Subject: Differential Equation

I need help with 4(a) and 4(b). Please show all the steps.

For problems #1-#4, I would suggest you use the template provided for you on Blackboard. #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, Xp, Yn» Yn+1 # 2.) Given the differential equation, y'=4cosx-3y, 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, xXn, Yn, Y1, M1, M2, M, yn41 6. #3.) Given the differential equation, y'=4cos x-3y, y(0)=1, 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 Please provide the following columns: n, Xn, Yn, M1, M2, M3, M М» М, Уп+1 4' # 4.) Given the differential equation, y'=4cosx-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. Problem #4 Exact Value found in Problem #4??.) to be y (?) = ?? Euler's Method Approximate Value Relative Error Percent Error h = ? h = ?? h = ??? Euler's Improved Method h = ? Approximate Value Relative Error Percent Error ii = 4 h = ??? Runge-Kutta Approximate Value Relative Error Percent Error ii = 4
Transcribed Image Text:For problems #1-#4, I would suggest you use the template provided for you on Blackboard. #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, Xp, Yn» Yn+1 # 2.) Given the differential equation, y'=4cosx-3y, 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, xXn, Yn, Y1, M1, M2, M, yn41 6. #3.) Given the differential equation, y'=4cos x-3y, y(0)=1, 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 Please provide the following columns: n, Xn, Yn, M1, M2, M3, M М» М, Уп+1 4' # 4.) Given the differential equation, y'=4cosx-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. Problem #4 Exact Value found in Problem #4??.) to be y (?) = ?? Euler's Method Approximate Value Relative Error Percent Error h = ? h = ?? h = ??? Euler's Improved Method h = ? Approximate Value Relative Error Percent Error ii = 4 h = ??? Runge-Kutta Approximate Value Relative Error Percent Error ii = 4
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