 5.4.1E: In 1 and 2, verify that the pair x (t) , y (t) is a solution to the...
 5.4.2E: In 1 and 2, verify that the pair x (t) , y (t) is a solution to the...
 5.4.3E: In 3–6, find the critical point set for the given system.
 5.4.4E: In 3–6, find the critical point set for the given system.
 5.4.5E: In 3–6, find the critical point set for the given system.
 5.4.6E: In 3–6, find the critical point set for the given system.
 5.4.7E: In 7–9, solve the phase plane equation (2), page 264, for the given...
 5.4.8E: In 7–9, solve the phase plane equation (2), page 264, for the given...
 5.4.9E: In 7–9, solve the phase plane equation (2), page 264, for the given...
 5.4.10E: Find all the critical points of the system and the xyphase plane s...
 5.4.11E: In 11–14, solve the phase plane equation for the given system. Then...
 5.4.12E: In 11–14, solve the phase plane equation for the given system. Then...
 5.4.13E: In 11–14, solve the phase plane equation for the given system. Then...
 5.4.14E: In 11–14, solve the phase plane equation for the given system. Then...
 5.4.15E: In 15–18, find all critical points for the given system. Then use a...
 5.4.16E: In 15–18, find all critical points for the given system. Then use a...
 5.4.17E: In 15–18, find all critical points for the given system. Then use a...
 5.4.18E: In 15–18, find all critical points for the given system. Then use a...
 5.4.19E: In 19–24, convert the given secondorder equation into a firstorde...
 5.4.20E: In 19–24, convert the given secondorder equation into a firstorde...
 5.4.21E: In 19–24, convert the given secondorder equation into a firstorde...
 5.4.22E: In 19–24, convert the given secondorder equation into a firstorde...
 5.4.23E: In 19–24, convert the given secondorder equation into a firstorde...
 5.4.24E: In 19–24, convert the given secondorder equation into a firstorde...
 5.4.25E: Using software, sketch the direction field in the phase plane for t...
 5.4.26E: Using software, sketch the direction field in the phase plane for t...
 5.4.27E: Using software, sketch the direction field in the phase plane for t...
 5.4.28E: Figure 5.16 displays some trajectories for the system What types of...
 5.4.29E: The phase plane diagrams depicted in Figure 5.12 were derived from ...
 5.4.30E: A proof of Theorem 1, page 268, is outlined below. The goal is to s...
 5.4.31E: Phase plane analysis provides a quick derivation of the energy inte...
 5.4.32E: Use the result of to prove that all solutions to the equation remai...
 5.4.33E: A Current Interest. The motion of an iron bar attracted by the magn...
 5.4.34E: Falling Object. The motion of an object moving vertically through t...
 5.4.35E: Sticky Friction. An alternative for the damping friction model F = ...
 5.4.36E: Rigid Body Nutation. Euler’s equations describe the motion of the p...
Solutions for Chapter 5.4: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 5.4
Get Full SolutionsChapter 5.4 includes 36 full stepbystep solutions. Since 36 problems in chapter 5.4 have been answered, more than 55368 students have viewed full stepbystep solutions from this chapter. This 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. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730.

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Binomial probability
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n  k2!pk11  p) nk where p is the probability of the outcome occurring once

Combination
An arrangement of elements of a set, in which order is not important

Constant term
See Polynomial function

Cubic
A degree 3 polynomial function

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Equivalent arrows
Arrows that have the same magnitude and direction.

Fibonacci numbers
The terms of the Fibonacci sequence.

First octant
The points (x, y, z) in space with x > 0 y > 0, and z > 0.

Linear system
A system of linear equations

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

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.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true

Spiral of Archimedes
The graph of the polar curve.

Variable
A letter that represents an unspecified number.

Variation
See Power function.