Explanation Given: The system of equations is, x ′ = 3 x + y − z ... ( 1 ) y ′ = x + 2 y − z ( 2 ) z ′ = 3 x + 3 y − z .... ( 3 ) Approach: Reduce the system of three equations in unknowns x ( t ) , y ( t ) and z ( t ) into a system of two equations with two unknowns x ( t ) and y ( t ) . Eliminate x from the reduced system of equations and solve for y to obtain a general solution for y ( t ) . Using the value of y ( t ) , find the general solution for x ( t ) and z ( t ) . Calculation: The system expressed in operator notation is as follows: ( D − 3 ) [ x ] − y + z = 0 − x + ( D − 2 ) [ y ] + z = 0 − 3 x − 3 y + ( D + 1 ) z = 0 ( 4 ) Eliminate z from the first two equations of system ( 4 ) by subtracting the second equation from the first equation ( D − 3 ) [ x ] − y + z + x − ( D − 2 ) [ y ] − z = 0 ( D − 2 ) [ x ] − ( D − 1 ) [ y ] = 0 .... ( 5 ) Eliminate z from the last two equations of system ( 4 ) by multiplying the second equation by ( D + 1 ) and subtracting from the third equation. − ( D + 1 ) x + ( D + 1 ) ( D − 2 ) [ y ] + ( D + 1 ) z + 3 x + 3 y − ( D + 1 ) z = 0 − ( D − 2 ) [ x ] + ( D 2 − D + 1 ) [ y ] = 0 ( 6 ) Eliminate x from the 2 × 2 system of equations ( 5 ) and ( 6 ) to get the following equation: ( D 2 − 2 D + 2 ) [ y ] = 0 which has the general solution y ( t ) = e t ( C 1 cos t + C 2 sin t ) ( 7 ) where C 1 and C 2 are arbitrary constants

7th Edition

ISBN: 9780321977175

Author: Nagle

Publisher: PEARSON CO

See similar textbooks

Videos

Question

Chapter 5.2, Problem 26E

To determine

To find:

A general solution for the given system of three equations using elimination method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.2, Problem 25E

Chapter 5.2, Problem 27E

Students have asked these similar questions

B1 The x distribution is a special case of Gamma distribution (not to be confused with gamma function; see below). The density function of the Gamma distribution with parameters and k is given by where -1 e -x/0 (x) = = г(k) Øk if x > 0, and otherwise, г(k) = √ ₁ k-1-x dx x' e is the gamma function. (a) For every k ≥ 1, 0 > 0, find the mode of the density. Hint: The algebra can be simplified by appropriate use of logarithms. ~ Now suppose that X1,..., Xn id Exp(\) and that we have a prior belief in A which is consistent with a prior distribution X. Gamma(a, b), for some a, ß, i.e. the prior density of is Baxa-1-BA T(a) e = so 01/ẞ and k = a. (b) Write down the likelihood, and show that the posterior distribution for \ is also a Gamma distribution, but with parameters a +n and B + Σ Xi. (c) Find the mode of the posterior distribution and examine the behaviour as n → ∞.

SCIE 211 Lab 3: Graphing and DataWorksheetPre-lab Questions:1. When should you use each of the following types of graphs? Fill answers in the table below.Type of Graph Used to showLine graphScatter plotBar graphHistogramPie Chart2. Several ways in which we can be fooled or misled by a graph were identified in the Lab 3Introduction. Find two examples of misleading graphs on the Internet and paste them below. Besure to identify why each graph is misleading. Data Charts:Circumference vs. Diameter for circular objectsDiameter Can 1 (cm) Can 2 (cm) Can 3 (cm)Trial 1Trial 2Trial 3MeanCircumference Can 1 (cm) Can 2 (cm) Can 3 (cm)Trial 1Trial 2Trial 3MeanScatter Plot Graph – Circumference Vs. DiameterIdentify 2 points of the Trendline.Y1 = ________ Y2 = _________X1 = ________ X2 = _________Calculate the Slope of the Trendline = Post-lab Questions:1. Answer the questions below. You will need to use the following equation to answer…

ix.com/math/grade-6/area-of-compound-figures-with-triangles Play Prodigy E May include: A blue... Play Prodigy Settings - About Chr... Analytics G one one-G What is the area of this figure? 3 yd 4 yd 6 yd 9 yd 9 yd 18 yd Write your answer using decimals, if necessary. square yards Submit esc -> C Desk 1 5 yd Work it out Not feeling ready yet? These can help

Chapter 5 Solutions

EBK FUND.OF DIFF.EQUATIONS+BOUNDARY...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

A general solution for the given system of three equations using elimination method.

Solution Summary: The author explains how to find a general solution for the given system of three equations using elimination method.

Videos

To find: A general solution for the given system of three equations using elimination method.

Want to see the full answer?

Chapter 5 Solutions

To find:

A general solution for the given system of three equations using elimination method.