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A First Course in Differential Equ...

11th Edition
Dennis G. Zill
Publisher: Cengage Learning
ISBN: 9781305965720
BuyFind

A First Course in Differential Equ...

11th Edition
Dennis G. Zill
Publisher: Cengage Learning
ISBN: 9781305965720

Solutions

Chapter
Section
Chapter 8.2, Problem 36E
Textbook Problem

In Problems 35–46 find the general solution of the given system.

d x d t = x + y d y d t = 2 x y

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Chapter 8 Solutions

A First Course in Differential Equations with Modeling Applications (MindTap Course List)
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 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 - 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 - Distinct Real Eigenvalues In Problems 112 find 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 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 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 - 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 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 - In problem 3132 solve the given initial-value...Ch. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Find phase portraits for the systems in Problems...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 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 - 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 - 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 - The system of mixing tanks shown in Figure 8.2.7...Ch. 8.2 - For the linear system in Problem 49: (a) Show that...Ch. 8.2 - 38. dxdt=4x+5ydydt=2x+6y 39. X = (4554)X 40. X =...Ch. 8.2 - Solve each of the following linear systems. (a)...Ch. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Obtain a Cartesian equation of the curve defined...Ch. 8.2 - Examine your phase portraits in Problem 51. Under...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 - 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 - 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 - In Problems 9 and 10, solve the given...Ch. 8.3 - In Problems 9 and 10, solve the given...Ch. 8.3 - Consider the large mixing tanks shown in Figure...Ch. 8.3 - (a) The system of differential equations for the...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 - 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 - 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 - 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 - 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 - 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 - 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 - In Problems 33 and 34 use (14) to solve the given...Ch. 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 - If y1 and y2 are linearly independent solutions of...Ch. 8.4 - In problem 1 and 2 use (3) to compute eAt and...Ch. 8.4 - In problem 1 and 2 use (3) to compute eAt and...Ch. 8.4 - In problem 3 and 4 use (3) to compute eAt. 3....Ch. 8.4 - In problem 3 and 4 use (3) to compute eAt. 4....Ch. 8.4 - In problem 58 use (1) use to find the general...Ch. 8.4 - In problem 58 use (1) use to find the general...Ch. 8.4 - In problem 58 use (1) use to find the general...Ch. 8.4 - In problem 58 use (1) to find the general solution...Ch. 8.4 - In problem 912 use (5) to find the general...Ch. 8.4 - In problem 912 use (5) to find the general...Ch. 8.4 - In problem 912 use (5) to find the general...Ch. 8.4 - In problem 912 use (5) to find the general...Ch. 8.4 - Solve the system in Problem 7 subject to the...Ch. 8.4 - Solve the system in Problem 9 subject to the...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 - 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 - Let P denote a matrix whose columns are...Ch. 8.4 - Let P denote a matrix whose columns are...Ch. 8.4 - Suppose A = PDP1 where D is defined as in (9). Use...Ch. 8.4 - If D is defined as in (9), then find eDt.Ch. 8.4 - In Problems 23 and 24 use the results of Problems...Ch. 8.4 - In Problems 23 and 24 use the results of Problems...Ch. 8.4 - Reread the discussion leading to the result given...Ch. 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 - In Problems 514 solve the given linear system. 9....Ch. 8 - In Problems 514 solve the given linear system. 10....Ch. 8 - In Problems 514 solve the given linear system. 11....Ch. 8 - In Problems 514 solve the given linear system. 12....Ch. 8 - In Problems 514 solve the given linear system. 13....Ch. 8 - In Problems 514 solve the given linear system. 14....Ch. 8 - (a) Consider the linear system X = AX of three...Ch. 8 - Verify that X'=(c1c2)et is a solution of the...

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