Question: Reduction of Order: Second Solution Use the steps o r the formula for y2 developed in Problem 75 to find a second linearly independent solution

Reduction of Order: Second Solution Use the steps o r the formula for y2 developed in Problem 75 to find a second linearly independent solution to the second-order differential equations of Problems 1-3 for which y1 is a known solution. Put the DE in standard form before using the formula.
1. y′′ − 6y′ + 9y = 0 , y1 = e3t
2. y′′ − 4y′ + 4y = 0, y1 = e2t
3. t2y′′ − ty′ + y = 0 , y1 = t

Step by Step Solution

★★★★★

3.42 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Reduction of Order Second Solution 1 y 6y 9y 0 y 1 e 3t We identify pt 6 so pt dt 6t Substituting in ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

947-M-L-A-L-S (4867).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Reduction of Order: Suppose you know one solution u1(x) to the second order homogeneous differential equation u" + a(x)u + b(x)u = 0. (a) Show that if u(x) = v(x) u1(x) is any other solution, then...

In problem the indicated function y 1 (x) is a solution of the given differential equation. Use reduction of order or formula (5), as instructed, to find a second solution y 2 (x). y'' - 4y' + 4y =...

Q1: Write the general solution of the differential equations: (a) 2y" + 10y = 4y (b) 64y" = 16y' - y (c) 3y" + 12y' = 0 (d) y"" - 5y" - 6y' = 0One solution to the differential equation tly" + 6ty' +...

Question 1 One solution to the differential equation tly" + 6ty' + 6y = 0,t > 0, is y =t-2. (a) Use the Reduction of Order Formula to find a second solution yz that is linearly independent to y1. (b)...

SOLVE Questions 1-5: PLEASE AND THANK YOU 1: What is the difference between homogenous and non-homogenous differential equation? Write an example for each and solve it. 2: What is the main formula to...

Downloaded 02/28/15 to 132.174.255.3. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 15.7. Exercises 475 changes and we laugh no more. While...

A. B. A. B. ( ( ) ) Beginning and Intermediate Algebra An open source (CC-BY) textbook Available for free download at: http://wallace.ccfaculty.org/book/book.html by Tyler Wallace 1 ISBN...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

A tensile testing machine is shown in the following figure to determine the behavior of materials as they are deformed. (a) Use the provided data to calculate the stress and the corresponding strain...

The figure shows recent data on x = the number of televisions per 100 people and y = the birth rate (number of births per 1000 people) for six African and Asian nations. The regression line,...

Using pycharm for hp create a code using FAKER 1 0 0 0 that will give me 1 0 0 0 fake data for each of the following categories Name Address Phone Email Age Please give step by step instructions for...

Henry Lile owned a house. When the land on which it was situated was condemned for a highway, he moved the house to the land of his daughter, Sarah Crick. In the course of construction work, blasting...

Find the inverse Laplace transform f (t) of each function given in Problems 1 through 10. Then sketch the graph of f. F(s) = -S s+2

Apply the definition in (1) to find directly the Laplace transforms of the functions described (by formula or graph) in Problems 1 through 10. f(t) = e 3t + 1

Find the convolution f(t) * g(t) in Problems 1 through 6. f(t) = g(t) = sin t

Computer Science II func. assignment #2 This is an example of a function where, (in the function) you read in 3 numbers, do a calculation, and return a value Write a C function that will: Determine...

The price of Microsolt (MSFT) today is $100 per share. MSFT has committed to make a $10.00 dividend payment in two years. The 0.0. risk-tree interest rate is flive percent. Assume there is no...

undefined Question 3. What happens on the balance sheets of banking system and the Fed, when the Fed make $ 75 million loan to First National Bank: (20 p.) a. Banking System (10 p.) Banking System...