I need help with Problem #4.Please show all the steps. The attached chart sheet is for #4(c). Please fill out that chart. Thank you! 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=0.5b.) Use Euler's Method to approximate the value of y(0.5) using h=0.1c.) Use Euler's Method to approximate the value of y(0.5) using h=0.05Please 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=0.5b.) Use Euler's Improved Method to approximate the value of y(0.5) using h=0.1c.) Use Euler's Improved Method to approximate the value of y(0.5) using h=0.05Please provide the following columns: n, xXn, Yn, Y1, M1, M2, M, yn416.#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=0.5b.) Use R-K, 4th-Order Method to approximate the value of y(0.5) using h=0.1c.) Use R-K, 4th-Order Method to approximate the value of y(0.5) using h=0.05Please provide the following columns: n, Xn, Yn, M1, M2, M3, MМ» М, Уп+14'# 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 yourproblems, #1 – #3.Problem #4Exact Value found in Problem #4??.) to be y (?) = ??Euler's MethodApproximate ValueRelative ErrorPercent Errorh = ?h = ??h = ???Euler's Improved Methodh = ?Approximate ValueRelative ErrorPercent Errorii = 4h = ???Runge-KuttaApproximate ValueRelative ErrorPercent Errorii = 4

Given: y'=4cosx-3y, y(0)=1 y'+3y=4cosx P(x)=3, Q(x)=4cosx P.I=e∫p(x)dx=e∫3dx=e3x Now,…

# 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.

# 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.

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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Question

I need help with Problem #4.

Please show all the steps. The attached chart sheet is for #4(c). Please fill out that chart. Thank you!

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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