 4.2.1E: In 1–12, find a general solution to the given differential equation.
 4.2.2E: In 1–12, find a general solution to the given differential equation.
 4.2.3E: In 1–12, find a general solution to the given differential equation.
 4.2.4E: In 1–12, find a general solution to the given differential equation.
 4.2.5E: In 1–12, find a general solution to the given differential equation.
 4.2.6E: In 1–12, find a general solution to the given differential equation.
 4.2.7E: In 1–12, find a general solution to the given differential equation.
 4.2.8E: In 1–12, find a general solution to the given differential equation.
 4.2.9E: In 1–12, find a general solution to the given differential equation.
 4.2.10E: In 1–12, find a general solution to the given differential equation.
 4.2.11E: In 1–12, find a general solution to the given differential equation.
 4.2.12E: In 1–12, find a general solution to the given differential equation.
 4.2.13E: In 13–20, solve the given initial value problem.
 4.2.14E: In 13–20, solve the given initial value problem.
 4.2.15E: In 13–20, solve the given initial value problem.
 4.2.16E: In 13–20, solve the given initial value problem.
 4.2.17E: In 13–20, solve the given initial value problem.
 4.2.18E: In 13–20, solve the given initial value problem.
 4.2.19E: In 13–20, solve the given initial value problem.
 4.2.20E: In 13–20, solve the given initial value problem.
 4.2.21E: FirstOrder ConstantCoefficient Equations.(a) Substituting y = ert...
 4.2.22E: In 22–25, use the method described in to find a general solution to...
 4.2.23E: In 22–25, use the method described in to find a general solution to...
 4.2.24E: In 22–25, use the method described in to find a general solution to...
 4.2.25E: In 22–25, use the method described in to find a general solution to...
 4.2.26E: Boundary Value Problems. When the values of a solution to a differe...
 4.2.27E: In 27–32, use Definition 1 to determine whether the functions y1 an...
 4.2.28E: In 27–32, use Definition 1 to determine whether the functions y1 an...
 4.2.29E: In 27–32, use Definition 1 to determine whether the functions y1 an...
 4.2.30E: In 27–32, use Definition 1 to determine whether the functions y1 an...
 4.2.31E: In 27–32, use Definition 1 to determine whether the functions y1 an...
 4.2.32E: In 27–32, use Definition 1 to determine whether the functions y1 an...
 4.2.33E: Explain why two functions are linearly dependent on an interval I i...
 4.2.34E: Wronskian. For any two differentiable functions y1 and y2 , the fun...
 4.2.35E: Linear Dependence of Three Functions. Three Functions y1(t) ,y2(t),...
 4.2.36E: Using the definition in 35, prove that if r1, r2 and,r3 , and are d...
 4.2.37E: In 37–41, find three linearly independent solutions (see 35) of the...
 4.2.38E: In 37–41, find three linearly independent solutions (see 35) of the...
 4.2.39E: In 37–41, find three linearly independent solutions (see 35) of the...
 4.2.40E: In 37–41, find three linearly independent solutions (see 35) of the...
 4.2.41E: In 37–41, find three linearly independent solutions (see 35) of the...
 4.2.43E: Solve the initial value problem:
 4.2.44E: Solve the initial value problem:
 4.2.45E: By using Newton’s method or some other numerical procedure to appro...
 4.2.46E: One way to define hyperbolic functions is by means of differential ...
Solutions for Chapter 4.2: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 4.2
Get Full SolutionsThis textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since 45 problems in chapter 4.2 have been answered, more than 68579 students have viewed full stepbystep solutions from this chapter. Chapter 4.2 includes 45 full stepbystep solutions. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This expansive textbook survival guide covers the following chapters and their solutions.

Absolute value of a vector
See Magnitude of a vector.

Constraints
See Linear programming problem.

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Imaginary part of a complex number
See Complex number.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Monomial function
A polynomial with exactly one term.

Nappe
See Right circular cone.

nth root
See Principal nth root

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Product of complex numbers
(a + bi)(c + di) = (ac  bd) + (ad + bc)i

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Reciprocal function
The function ƒ(x) = 1x

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Third quartile
See Quartile.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.