 4.8.1E: Show that if y(t) satisfies then y(t) satisfies
 4.8.2E: Using the paradigm (13), what are the inertia, damping, and stiffne...
 4.8.3E: Try to predict the qualitative features of the solution to that sat...
 4.8.4E: Show that the three solutions and to are linearly independent on (...
 4.8.5E: (a) Use the energy integral lemma to derive the family of solutions...
 4.8.6E: Use the energy integral lemma to show that motions of the free unda...
 4.8.7E: Pendulum Equation. To derive the pendulum equation (21), complete t...
 4.8.8E: Use the energy integral lemma to show that pendulummotions obey
 4.8.9E: Use the result of to find the value of ?’(0), the initial velocity,...
 4.8.10E: Use the result of to prove that if the pendulum in Figure 4.18 is r...
 4.8.11E: Use the mass–spring analogy to explain the qualitative nature of th...
 4.8.12E: Use reduction of order to derive the solution y2(t) in equation (5)...
 4.8.13E: Figure 4.26 contains graphs of solutions to the Duffing, Airy, and ...
 4.8.14E: Verify that the formulas for the Bessel functions J1/2(t),Y1/2(t) d...
 4.8.15E: Use the mass–spring oscillator analogy to decide whether all soluti...
 4.8.16E: Use the energy integral lemma to show that every solution to the Du...
 4.8.17E: Armageddon. Earth revolves around the sun in an approximately circu...
Solutions for Chapter 4.8: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 4.8
Get Full SolutionsThis textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Chapter 4.8 includes 17 full stepbystep solutions. Since 17 problems in chapter 4.8 have been answered, more than 56868 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Direct variation
See Power function.

Empty set
A set with no elements

Event
A subset of a sample space.

Fivenumber summary
The minimum, first quartile, median, third quartile, and maximum of a data set.

Hypotenuse
Side opposite the right angle in a right triangle.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Second
Angle measure equal to 1/60 of a minute.

Sine
The function y = sin x.

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Tangent
The function y = tan x

Unit vector
Vector of length 1.

Zero factor property
If ab = 0 , then either a = 0 or b = 0.