A First Course in Differential Equations with Modeling Applications (MindTap Course List)
11th Edition
ISBN: 9781305965720
Author: Dennis G. Zill
Publisher: Cengage Learning
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Textbook Question
Chapter 8.1, Problem 21E
In Problems 21–24 verify that the
21.
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7.
Invert the following matrix
3x – 2y = 9
-x + 3y = 3
|
9.
P =
15
-4
-7
2e31 – 8e-
-4e31 + 2e-
ž(1) = |
3e3t – 20e-
-6e31 + 5et
Show that x1 (t) is a solution to the system x = Px by evaluating derivatives and the
matrix product
-4
ž(1) = | 15 -7
Enter your answers in terms of the variable t.
Show that x2(t) is a solution to the system x' = Px by evaluating derivatives and the
matrix product
9.
3(1) = | 15
-4
X2(t)
-7
Enter your answers in terms of the variable t.
2. Given the following 2 x 2 linear system with constant coefficients
x' = Ax
(H)
x= Ax+g(t), (N)
where g is not the zero vector. Which of the following statements are true? Justify your
answers.
A. If , is a solution to (H) and 7, is a solution to (N), then , +27, is a solution to
(N).
B. If , and 2 are both solutions to (N), then ₁-2 is a solution to (H).
Chapter 8 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
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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- 4. (S.10). Use Gaussian elimination with backward substitution to solve the following linear system: 2.r1 + 12 – 13 = 5, 1 + 12 – 3r3 = -9, -I1 + 12 +2r3 = 9;arrow_forward2. Which of the following is a general solution to the following: x²y" + xy' + (36x² - 1) y (Hint: As discussed in the lecture, use Y, only when J, and J-, are linearly dependent). A. y = c₁J₁(2x) + C₂J_1(2x) 6 B. y = C₁J₁(x) + C₂Y₁(x) 3 3 C. y = c₁₂/₁(6x) + C₂Y₁(6x) 0 D. y = c₁J₁(6x) + c₂] _1(6x) 2arrow_forward15. If A=| B = 0 1 and C = 1 0 , then find the matrix (A v B) 0 carrow_forward
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