- 1.3.1E: The direction field for dy/dx = 2x + y is shown in Figure 1.12.(a) ...
- 1.3.2E: The direction field for is shown in dy/dx = 4x/y Figure 1.13.(a) Ve...
- 1.3.3E: A model for the velocity v at time t of a certain object falling un...
- 1.3.4E: If the viscous force in is nonlinear, a possible model would be pro...
- 1.3.5E: The logistic equation for the population (in thousands) of a certai...
- 1.3.6E: Consider the differential equation (a) A solution curve passes thro...
- 1.3.7E: Consider the differential equation for the population p (in thousan...
- 1.3.8E: The motion of a set of particles moving along the x-axis is governe...
- 1.3.9E: Let denote the solution to the initial value problem (a) Show that ...
- 1.3.10E: Use a computer software package to sketch the direction field for t...
- 1.3.11E: In 11–16, draw the isoclines with their direction markers and sketc...
- 1.3.12E: In 11–16, draw the isoclines with their direction markers and sketc...
- 1.3.13E: In the problem below, draw the isoclines with their direction marke...
- 1.3.14E: In 11–16, draw the isoclines with their direction markers and sketc...
- 1.3.15E: In 11–16, draw the isoclines with their direction markers and sketc...
- 1.3.16E: In 11–16, draw the isoclines with their direction markers and sketc...
- 1.3.17E: From a sketch of the direction field, what can one say about the be...
- 1.3.18E: From a sketch of the direction field, what can one say about the be...
- 1.3.19E: By rewriting the differential equation dy/dx = - y/x in the form in...
- 1.3.20E: A bar magnet is often modeled as a magnetic dipole with one end lab...
Solutions for Chapter 1.3: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations | 8th Edition
Additive identity for the complex numbers
0 + 0i is the complex number zero
Additive inverse of a complex number
The opposite of a + bi, or -a - bi
See Inverse tangent function.
The real number multiplied by the variable(s) in a polynomial term
Components of a vector
See Component form of a vector.
A statement that describes a bounded interval, such as 3 ? x < 5
Explicitly defined sequence
A sequence in which the kth term is given as a function of k.
Connected subset of the real number line with at least two points, p. 4.
Limit to growth
See Logistic growth function.
Measure of an angle
The number of degrees or radians in an angle
See Absolute value of a complex number.
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.
Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)
Polar form of a complex number
See Trigonometric form of a complex number.
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.
A set of ordered pairs of real numbers.
Zeros of multiplicity ? 2 (see Multiplicity).
A function that can be written in the form f(x) = a sin (b (x - h)) + k or f(x) = a cos (b(x - h)) + k. The number a is the amplitude, and the number h is the phase shift.
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 numbers 0, 1, 2, 3, ... .