First Course in Differential Equations (Instructor's)
11th Edition
ISBN: 9781305965775
Author: ZILL
Publisher: CENGAGE L
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Textbook Question
Chapter 8.2, Problem 2E
In Problems 1–12 find the general solution of the given system.
2.
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In Problems 19–56, solve each system of equations. If the system has no solution, say that it is inconsistent. For Problems 19–30, graphthe lines of the system
1. Y = 5x + 2
2. 5y = 25x + 10
%3D
3. 5y = 10x + 10
4. 2y = 10x – 4
Which pair of equations forms a system that has infinitely many solutions?
2 and 4
2 and 3
O 1 and 2
O 1 and 4
Problems 74–77 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your
mind so that you are better prepared for the final exam.
74. To graph g(x) = |x + 2| – 3, shift the graph of
f(x) = \x|
units
76. Solve: logs (x + 3) = 2
units
and then
77. Solve the given system using matrices.
number
Teft/right|
number
up/down
Зх + у + 2z %3 1
75. Find the rectangular coordinates of the point whose polar
2x – 2y + 5z =
5
x + 3y + 2z = -9
coordinates are ( 6,
3
Chapter 8 Solutions
First Course in Differential Equations (Instructor's)
Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 6ECh. 8.1 - In Problems 710 write the given linear system...Ch. 8.1 - In Problems 710 write the given linear system...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 10E
Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - Prob. 12ECh. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - Prove that the general solution of the homogeneous...Ch. 8.1 - Prove that the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - Prob. 4ECh. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 1-12 find...Ch. 8.2 - In Problems 13 and 14 solve the given...Ch. 8.2 - In Problems 13 and 14 solve the given...Ch. 8.2 - In Problem 27 of Exercises 4.9 you were asked to...Ch. 8.2 - (a) Use computer software to obtain the phase...Ch. 8.2 - Find phase portraits for the systems in Problems 2...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In problem 2130 find the general solution of the...Ch. 8.2 - In problem 3132 solve the given initial-value...Ch. 8.2 - Prob. 32ECh. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Prob. 34ECh. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 35 46 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 47 and 48 solve the given...Ch. 8.2 - In Problems 47 and 48 solve the given...Ch. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - 38. dxdt=4x+5ydydt=2x+6y 39. X = (4554)X 40. X =...Ch. 8.2 - Prob. 53ECh. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Prob. 55ECh. 8.2 - Examine your phase portraits in Problem 51. Under...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 2ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 6ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 9 and 10, solve the given...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - (a) The system of differential equations for the...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 14ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 16ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 31ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 33ECh. 8.3 - In Problems 33 and 34 use (14) to solve the given...Ch. 8.3 - The system of differential equations for the...Ch. 8.3 - Prob. 36ECh. 8.4 - In problem 1 and 2 use (3) to compute eAt and...Ch. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - In problem 912 use (5) to find the general...Ch. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - Prob. 18ECh. 8.4 - Let P denote a matrix whose columns are...Ch. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - A matrix A is said to be nilpotent if there exists...Ch. 8 - fill in the blanks. 1. The vector X=k(45) is a...Ch. 8 - fill in the blanks. The vector...Ch. 8 - Consider the linear system X=(466132143)X. Without...Ch. 8 - Consider the linear system X = AX of two...Ch. 8 - In Problems 514 solve the given linear system. 5....Ch. 8 - In Problems 514 solve the given linear system. 6....Ch. 8 - In Problems 514 solve the given linear system. 7....Ch. 8 - In Problems 514 solve the given linear system. 8....Ch. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - In Problems 514 solve the given linear system. 11....Ch. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - (a) Consider the linear system X = AX of three...Ch. 8 - Prob. 16RE
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- 8. Use any method to find the general solution of the system x + 2 [1/₂].arrow_forwardH.W:- Solve The linear SysTem O 1.7X-3.2y = 81 014x+112y = -2 2X+X2- X3=D9 8 X2+ 6X3=-6 -2 X1+4x2-6X3= Y0 %3D ®2x+3y+2-1/W = | 5x -2y+5z-4w=S X-Y+32-3w=3 3ペナ9yーチスナ2w=ー7arrow_forwardQ.1. Explain why the linear system has no solution: 1 0 3 1 0 1 2 4 0 0 0 For which values ofk does the system below have a solution? x-3y = 6 + 3z = -3 2x + ky + (3 – k)z = 1arrow_forward
- 2. (10 points) Find the general solution of the following first order system. x = 5x1 – 6x2 + 3e² x2 = 3x1 – 4.x2 + et %3D -arrow_forward3. Find the general solution of the system given by Y2 + Y3 Y2 = Yı + Y3 (3) Yı + Y2 || || ||arrow_forward[1 1 1] 024. The system of equations | 0 0 1x=| b, | is solvable if |0 0 1 b, (c) b, = b, (d) b, = 0 (e) none (a) h, = b, = 0 (b) b, = b, # 0 025. If A = B+C and B= B' and C' =-C, then %3D %3D (1) C = A– A" »C=÷(4- A') (6) C=;(4+A") (4) C = A+ A" (e) none c=-(4-A') (0) C = (A+ A°) («)C= A+ A°arrow_forward
- 1. For which values of k will the following system have no solution? Exactly one solution? Infinitely many solutions? x + ky - 2z = 0 x + 2ky – 2z = 5 x + ky + (k^2 –- 3k)z = k – 1arrow_forward4. Use Gaussian elimination with backward substitution to solve the following linear system: 2x1 + x2 – x3 = 5, x1 + x2 – 3x3 = -9, -x1 + x2 + 2x3 = 9;arrow_forward. solve these systems of equations by graphing. SYS1-3 (y =-3x+6 ly = 2x-4 4. v=2x+3 [5x-y=6 3x-3y 6 2. (-2x-4y=-2 5. 4x+8y=4 yA (-4x+2y = 8 3. 6. ly=-x-1 [6x-3y=3 y a4 Cengage Learning All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole orarrow_forward
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