Question: Find the general real solution to the following homogeneous differential equations: (a) u + 4u = 0 (b) u + 6u' + 10u = 0

Find the general real solution to the following homogeneous differential equations:
(a) u" + 4u = 0
(b) u" + 6u' + 10u = 0
(c) 2u'" + 3u' - 5u = 0
(d) u"" + u = 0
(e) u"" + 13u" + 36u = 0
(f) x2 u" - xu′ + 3u = 0
(g) x3u'" + x2u" + 3xu' - 8u = 0

Step by Step Solution

★★★★★

3.43 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a ux c 1 cos 2x c 2 sin 2x b ux c 1 e 3x cos x c 2 e 3x sin x c ux c 1 ... 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)

952-M-L-A-E (2545).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Write out the formula for the general real solution to the system in Example 9.16 and verify its stability.

Find the general real solution to the following systems of differential equations: (a) (b) (c) (d) (e) = 4X1 + 3X2 X2 = 3X1-4X2 ,-- = 3x1-8x2 + 2x3 x2 =-u + 2x2 + 2x3 x3 = x1-4x2 + 2x3

Use the method Exercise 10.1.36 to find the general real solution to the following iterative systems: (a) u(k+1) = 2u(k) + 3v(k), v(k+1) = 2v(k) (b) u(k+1) = u(k) + v(k), v(k+1) = -4u(k) + 5v(k) (c)...

Find a finite set of real functions that spans the solution space to the following homogeneous ordinary differential equations: (a) u - 2u = 0 (b) u+ 4u = 0 (c) u - 3u= 0 (d) u + 4u+3u =0 (e) u + u +...

Problems 19, 22, 26, and 29!! 840b2c...: "Towar... Review Questions 1. Give the trial solution used to solve linear constant-coefficient 21. y" - 2y' + y = 0: y(0) = 4, y'(0) = 0 homogeneous...

Mid Term # 2 Question 1 [10 marks] Choose the correct answer: (i) The surface area of the cone frustum generated by revolving the line segment y = x 2 + 12 , 1 x 3 about the x axis is (a) 4 5 (b) 2...

MCV4U Vectors Lesson Assignment 3 In this assignment you are going to focus on: addition, subtraction, and multiplication of vectors. Total Marks: 55 marks Instructions: After completing the lesson...

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

write MATLAB scripts to solve differential equations. Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle Objective: Write MATLAB scripts to solve differential equations....

Direction: Answer the exercise and I provide some example or guide on how you do it. Imaginary Roots of Auxiliary Equations ye = Ci cos 2x + Czsin 2x So we have distinct real root (3), repeated real...

Your firm generally receives 3 cheques a month. A month is defined as a 30-day period. The cheque amounts and the collection delay for each cheque are shown below. Given this information, what is the...

Now, assume that you work in the internal audit function at a company that is considering a software package to help automate the process of complying with the requirements of the Sarbanes-Oxley Act...

During 2 0 2 4 , Vertex Industries sold 7 5 , 0 0 0 units of its only product for $ 3 2 per unit. Manufacturing and selling the product required $ 1 4 0 , 0 0 0 of fixed manufacturing costs and $ 2 4...

Define cross-price elasticity of demand. What does it mean if the cross-price elasticity of demand is negative? What does it mean if the cross-price elasticity of demand is positive?

George Wolford has suggested the following variation on the Linda problem (see Exercise 1.2.25). The registrar is carrying John and Marys registration cards and drops them in a puddle. When he picks...

Let Ri be the event that the ith player in a poker game has a royal flush. Show that a royal flush (A, K, Q, J, 10 of one suit) attracts another royal flush, that is P (R2|R1) > P (R2). Show that a...

Prove that A neither attracts nor repels B if and only if A and B are independent.

Help Please Complete the following table. Use (Round time value factors to 3 decimal places and final answers to the nearest whole number.) Exhibit 1-B Future value (compounded sum) of $1 paid in at...

Compute the expected return given these three economic states, their likelihoods, and the potential returns: (Round your answer to 2 decimal places.) Economic State Probability Return Fast growth...

Problem 1: According to the CAPM, what is the expected return on a security given a market risk premium of 12%, a stock beta of 1.44, and a risk free interest rate of 1%? Put the answers in decimal...