- 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
The case in which two sides and a nonincluded angle can determine two different triangles
See Power function.
A set with no elements
A subset of a sample space.
The minimum, first quartile, median, third quartile, and maximum of a data set.
Side opposite the right angle in a right triangle.
Point where a curve crosses the x-, y-, or z-axis in a graph.
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers
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,
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.
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.
Angle measure equal to 1/60 of a minute.
The function y = sin x.
Symmetric about the y-axis
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
The function y = tan x
Vector of length 1.
Zero factor property
If ab = 0 , then either a = 0 or b = 0.