 9.5.1E: In 1–8, find the eigenvalues and eigenvectors of the given matrix.
 9.5.2E: In 1–8, find the eigenvalues and eigenvectors of the given matrix.
 9.5.3E: In 1–8, find the eigenvalues and eigenvectors of the given matrix.
 9.5.4E: In 1–8, find the eigenvalues and eigenvectors of the given matrix.
 9.5.5E: In 1–8, find the eigenvalues and eigenvectors of the given matrix.
 9.5.6E: In 1–8, find the eigenvalues and eigenvectors of the given matrix.
 9.5.7E: In 1–8, find the eigenvalues and eigenvectors of the given matrix.
 9.5.8E: In 1–8, find the eigenvalues and eigenvectors of the given matrix.
 9.5.9E: In 9 and 10, some of the eigenvalues of the given matrix are comple...
 9.5.10E: In 9 and 10, some of the eigenvalues of the given matrix are comple...
 9.5.11E: In 11–16, find a general solution of the system x’ (t) = Ax (t) for...
 9.5.12E: In 11–16, find a general solution of the system x’(t) = Ax(t) for t...
 9.5.13E: In 11–16, find a general solution of the system x’(t) = Ax(t) for t...
 9.5.14E: In 11–16, find a general solution of the system x’(t) = Ax(t) for t...
 9.5.15E: In 11–16, find a general solution of the system x’(t) = Ax(t) for t...
 9.5.16E: In 11–16, find a general solution of the system x’(t) = Ax(t) for t...
 9.5.17E: Consider the system with
 9.5.18E: Consider the system with (a) Show that the matrix A has eigenvalues...
 9.5.19E: In 19–24, find a fundamental matrix for the system x’ (t) = Ax (t) ...
 9.5.20E: In 19–24, find a fundamental matrix for the system x’ (t) = Ax (t) ...
 9.5.21E: In 19–24, find a fundamental matrix for the system x’ (t) = Ax (t) ...
 9.5.22E: In 19–24, find a fundamental matrix for the system x’ (t) = Ax (t) ...
 9.5.23E: In 19–24, find a fundamental matrix for the system x’ (t) = Ax (t) ...
 9.5.24E: In 19–24, find a fundamental matrix for the system x’ (t) = Ax (t) ...
 9.5.25E: Using matrix algebra techniques, find a general solution of the system
 9.5.26E: Using matrix algebra techniques, find a general solution of the system
 9.5.27E: In 27–30, use a linear algebra software package such as MATLAB, MAP...
 9.5.28E: In 27–30, use a linear algebra software package such as MATLAB, MAP...
 9.5.29E: In 27–30, use a linear algebra software package such as MATLAB, MAP...
 9.5.30E: In 27–30, use a linear algebra software package such as MATLAB, MAP...
 9.5.31E: In 31–34, solve the given initial value problem.
 9.5.32E: In 31–34, solve the given initial value problem.
 9.5.33E: In 31–34, solve the given initial value problem.
 9.5.34E: In 31–34, solve the given initial value problem.
 9.5.35E: (a) Show that the matrix has the repeated eigenvalue r = 1 and tha...
 9.5.36E: Use the method discussed in to find a general solution to the system
 9.5.37E: (a) Show that the matrix has the repeated eigenvalue r = 2 with mul...
 9.5.38E: Use the method discussed in to find a general solution to the system
 9.5.39E: (a) Show that the matrix has the repeated eigenvalue r = 1 of multi...
 9.5.40E: Use the method discussed in to find a general solution to the syste...
 9.5.41E: Use the substitution x1 = y, x2 = y’ to convert the linear equation...
 9.5.42E: (a) Show that the Cauchy–Euler equation can be written as a Cauchy–...
 9.5.43E: In 43 and 44, use the result of to find a general solution of the g...
 9.5.44E: In 43 and 44, use the result of to find a general solution of the g...
 9.5.45E: Mixing Between Interconnected Tanks. Two tanks, each holding 50 L o...
 9.5.46E: Mixing with a Common Drain. Two tanks, each holding 1 L of liquid, ...
 9.5.47E: To find a general solution to the system proceed as follows: (a) Us...
 9.5.48E: To complete the proof of Theorem 6, assume the induction hypothesis...
 9.5.49E: Stability. A homogeneous system x’ = Ax with constant coefficients ...
 9.5.50E: In an ice tray, the water level in any particular ice cube cell wil...
Solutions for Chapter 9.5: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 9.5
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since 50 problems in chapter 9.5 have been answered, more than 66075 students have viewed full stepbystep solutions from this chapter. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. Chapter 9.5 includes 50 full stepbystep solutions.

Binomial
A polynomial with exactly two terms

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Central angle
An angle whose vertex is the center of a circle

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

Conditional probability
The probability of an event A given that an event B has already occurred

Constant term
See Polynomial function

Doubleangle identity
An identity involving a trigonometric function of 2u

Frequency distribution
See Frequency table.

Imaginary axis
See Complex plane.

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Modulus
See Absolute value of a complex number.

nth root of unity
A complex number v such that vn = 1

Pointslope form (of a line)
y  y1 = m1x  x 12.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Standard representation of a vector
A representative arrow with its initial point at the origin

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Wrapping function
The function that associates points on the unit circle with points on the real number line