 6.1.1E: In 1–6, determine the largest interval (a,b) for which Theorem 1 gu...
 6.1.2E: In 1–6, determine the largest interval (a,b) for which Theorem 1 gu...
 6.1.22E: In 19–22, a particular solution and a fundamental solution set are ...
 6.1.3E: In 1–6, determine the largest interval (a,b) for which Theorem 1 gu...
 6.1.4E: In 1–6, determine the largest interval (a,b) for which Theorem 1 gu...
 6.1.5E: In 1–6, determine the largest interval (a,b) for which Theorem 1 gu...
 6.1.6E: In 1–6, determine the largest interval (a,b) for which Theorem 1 gu...
 6.1.7E: In 7–14, determine whether the given functions are linearly depende...
 6.1.8E: In 7–14, determine whether the given functions are linearly depende...
 6.1.9E: In 7–14, determine whether the given functions are linearly depende...
 6.1.10E: In 7–14, determine whether the given functions are linearly depende...
 6.1.11E: In 7–14, determine whether the given functions are linearly depende...
 6.1.12E: In 7–14, determine whether the given functions are linearly depende...
 6.1.13E: In 7–14, determine whether the given functions are linearly depende...
 6.1.14E: In 7–14, determine whether the given functions are linearly depende...
 6.1.15E: Using the Wronskian in 15–18, verify that the given functions form ...
 6.1.16E: Using the Wronskian in 15–18, verify that the given functions form ...
 6.1.17E: Using the Wronskian in 15–18, verify that the given functions form ...
 6.1.18E: Using the Wronskian in 15–18, verify that the given functions form ...
 6.1.19E: In 19–22, a particular solution and a fundamental solution set are ...
 6.1.20E: In 19–22, a particular solution and a fundamental solution set are ...
 6.1.21E: In 19–22, a particular solution and a fundamental solution set are ...
 6.1.23E: Let and y2(x):=x. Verify that L[y1](x) = x sinx and L[y2](x) = x2+1...
 6.1.24E: Let and y2(x):= 1/3. Verify that and Then use the superposition pr...
 6.1.25E: Prove that L defined in (7) is a linear operator by verifying that ...
 6.1.26E: Existence of Fundamental Solution Sets. By Theorem 1, for each j = ...
 6.1.27E: Show that the set of functions {1,x,x2, . . . , xn}. where n is a p...
 6.1.28E: The set of functions { 1, cos x, sin x, . . . , cos nx, sin nx} whe...
 6.1.29E: (a) Show that if f1, . . . , fm are linearly independent On (1,1),...
 6.1.30E: To prove Abel’s identity (26) for n=3, proceed as follows:(a) Let U...
 6.1.31E: Reduction of Order. If a nontrivial solution f(x) is known for the ...
 6.1.32E: Given that the function f(x) =x is a solution to y’’’ – x2y’ + xy =...
 6.1.33E: Use the reduction of order method described in to find three linear...
 6.1.34E: Constructing Differential Equations. Given three Functions f1(x) ,f...
 6.1.35E: Use the result of to construct a third order differential equation ...
Solutions for Chapter 6.1: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 6.1
Get Full SolutionsFundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. Since 35 problems in chapter 6.1 have been answered, more than 61022 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Chapter 6.1 includes 35 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Dependent event
An event whose probability depends on another event already occurring

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

Exponential function
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

Finite series
Sum of a finite number of terms.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Length of an arrow
See Magnitude of an arrow.

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Polar equation
An equation in r and ?.

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Remainder polynomial
See Division algorithm for polynomials.

Scalar
A real number.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Vertex of a cone
See Right circular cone.