# 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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