Explanation Procedure used: Solution of system of differential equations by elimination method. 1 Consider the system of differential equations. 2 Express the equations in differential operator form. 3 Find the DE by elimination. 4 Obtain the complementary function. 5 Further, Obtain the particular solution. 6 Ultimately write the general solution in form y ( x ) = y c + y p . Calculation: Consider the system of differential equations d x d t = − x + z , d y d t = − y + z , d z d t = − x + y . Indicate the set of differential equation in differential operator form. ( D + 1 ) x − z = 0 … ( 1 ) ( D + 1 ) y − z = 0 … ( 2 ) x − y + D z = 0 … ( 3 ) Solve the equations ( 1 ) and ( 2 ) as ( 1 ) − ( 2 ) . Therefore, ( D + 1 ) x − ( D + 1 ) y = 0 … ( 4 ) Solve ( 2 ) and ( 3 ) as D × ( 2 ) + ( 3 ) . Thus, x + ( D 2 + D − 1 ) y = 0 … ( 5 ) Solve ( 4 ) and ( 5 ) as ( 4 ) × ( D 2 + D − 1 ) + ( 5 ) × ( D + 1 ) . Thus, ( D 2 + D − 1 ) ( D + 1 ) x + ( D + 1 ) x = 0 ( D + 1 ) ( D 2 + D ) x = 0 D ( D + 1 ) 2 ( x ) = 0 Find the roots of auxiliary equation associate to DE D ( D + 1 ) 2 ( x ) = 0 . Thus, m ( m + 1 ) 2 = 0 m 1 = 0 , m 2 = − 1 = m 3 Thus, the general solution is x ( t ) = c 1 + c 2 e − t + c 3 t e − t

Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term

11th Edition

ISBN: 9781337761000

Author: Dennis G. Zill

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 4.9, Problem 20E

To determine

To solve: The system of differential equations dxdt=−x+z,dydt=−y+z,dzdt=−x+y by systematic elimination.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.9, Problem 19E

Chapter 4.9, Problem 21E

Students have asked these similar questions

There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three investment? STEP 1: The formula for compound interest is A = nt = P(1 + − − ) n², where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to A = Pert Find r and n for each model, and use these values to write A in terms of t for each case. Annual Model r=0.10 A = Y(t) = 1150 (1.10)* n = 1 Quarterly Model r = 0.10 n = 4 A = Q(t) = 1150(1.025) 4t Continuous Model r=0.10 A = C(t) =…

The following ordered data list shows the data speeds for cell phones used by a telephone company at an airport: A. Calculate the Measures of Central Tendency from the ungrouped data list. B. Group the data in an appropriate frequency table. C. Calculate the Measures of Central Tendency using the table in point B. D. Are there differences in the measurements obtained in A and C? Why (give at least one justified reason)? I leave the answers to A and B to resolve the remaining two. 0.8 1.4 1.8 1.9 3.2 3.6 4.5 4.5 4.6 6.2 6.5 7.7 7.9 9.9 10.2 10.3 10.9 11.1 11.1 11.6 11.8 12.0 13.1 13.5 13.7 14.1 14.2 14.7 15.0 15.1 15.5 15.8 16.0 17.5 18.2 20.2 21.1 21.5 22.2 22.4 23.1 24.5 25.7 28.5 34.6 38.5 43.0 55.6 71.3 77.8 A. Measures of Central Tendency We are to calculate: Mean, Median, Mode The data (already ordered) is: 0.8, 1.4, 1.8, 1.9, 3.2, 3.6, 4.5, 4.5, 4.6, 6.2, 6.5, 7.7, 7.9, 9.9, 10.2, 10.3, 10.9, 11.1, 11.1, 11.6, 11.8, 12.0, 13.1, 13.5, 13.7, 14.1, 14.2, 14.7, 15.0, 15.1, 15.5,…

A tournament is a complete directed graph, for each pair of vertices x, y either (x, y) is an arc or (y, x) is an arc. One can think of this as a round robin tournament, where the vertices represent teams, each pair plays exactly once, with the direction of the arc indicating which team wins. (a) Prove that every tournament has a direct Hamiltonian path. That is a labeling of the teams V1, V2,..., Un so that vi beats Vi+1. That is a labeling so that team 1 beats team 2, team 2 beats team 3, etc. (b) A digraph is strongly connected if there is a directed path from any vertex to any other vertex. Equivalently, there is no partition of the teams into groups A, B so that every team in A beats every team in B. Prove that every strongly connected tournament has a directed Hamiltonian cycle. Use this to show that for any team there is an ordering as in part (a) for which the given team is first. (c) A king in a tournament is a vertex such that there is a direct path of length at most 2 to any…

Chapter 4 Solutions

Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Given that x(t) = c1 cos t + c2 sin t is the...Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

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.

The system of differential equations d x d t = − x + z , d y d t = − y + z , d z d t = − x + y by systematic elimination.

Solution Summary: The author explains how to solve the system of differential equations by systematic elimination.

Videos

To solve: The system of differential equations dxdt=−x+z,dydt=−y+z,dzdt=−x+y by systematic elimination.

Want to see the full answer?

Chapter 4 Solutions