# Subject: Differential equation show all the steps and me fill out the given spreadsheet for 4(c)

Subject: Differential equation show all the steps and me fill out the given spreadsheet for 4(c). I really need with this question. you! 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
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
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
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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