 4.1.11E: (a) Use the family in to find a solution of that satisfies the boun...
 4.1.1E: In 1–4 the given family of functions is the general solution of the...
 4.1.2E: In 1–4 the given family of functions is the general solution of the...
 4.1.3E: In 1–4 the given family of functions is the general solution of the...
 4.1.4E: In 1–4 the given family of functions is the general solution of the...
 4.1.5E: Given that y = c1 + c2x2 is a twoparameter family of solutions of ...
 4.1.6E: Find two members of the family of solutions in that satisfy the ini...
 4.1.7E:
 4.1.8E: Use the general solution of given in to show that a solution satisf...
 4.1.9E: In 9 and 10 find an interval centered about x = 0 for which the giv...
 4.1.10E: In 9 and 10 find an interval centered about x = 0 for which the giv...
 4.1.12E: Use the family in to find a solution of that satisfies the boundary...
 4.1.13E: In 13 and 14 the given twoparameter family is a solution of the in...
 4.1.14E: In 13 and 14 the given twoparameter family is a solution of the in...
 4.1.15E: In 15–22 determine whether the given set of functions is linearly i...
 4.1.16E: In 15–22 determine whether the given set of functions is linearly i...
 4.1.17E: In 15–22 determine whether the given set of functions is linearly i...
 4.1.18E: In 15–22 determine whether the given set of functions is linearly i...
 4.1.19E: In 15–22 determine whether the given set of functions is linearly i...
 4.1.20E: In 15–22 determine whether the given set of functions is linearly i...
 4.1.21E: In 15–22 determine whether the given set of functions is linearly i...
 4.1.22E: In 15–22 determine whether the given set of functions is linearly i...
 4.1.23E: In 23–30 verify that the given functions form a fundamental set of ...
 4.1.24E: In 23–30 verify that the given functions form a fundamental set of ...
 4.1.25E: In 23–30 verify that the given functions form a fundamental set of ...
 4.1.26E: In 23–30 verify that the given functions form a fundamental set of ...
 4.1.27E: In 23–30 verify that the given functions form a fundamental set of ...
 4.1.28E: In 23–30 verify that the given functions form a fundamental set of ...
 4.1.29E: In 23–30 verify that the given functions form a fundamental set of ...
 4.1.30E: In 23–30 verify that the given functions form a fundamental set of ...
 4.1.31E: In 31–34 verify that the given twoparameter family of functions is...
 4.1.32E: In 31–34 verify that the given twoparameter family of functions is...
 4.1.33E: In 31–34 verify that the given twoparameter family of functions is...
 4.1.34E: In 31–34 verify that the given twoparameter family of functions is...
 4.1.35E:
 4.1.36E: (a) By inspection find a particular solution of (b) By inspection f...
 4.1.37E: Let n = 1, 2, 3, . . . . Discuss how the observations Dnxn1 = 0 an...
 4.1.38E: Suppose that y1 = ex and y2 = ex are two solutions of a homogeneou...
 4.1.39E: (e) By the superposition principle, Theorem 4.1.2, both linear comb...
 4.1.40E: Is the set of functions linearly dependent or linearly independent ...
 4.1.41E: Suppose y1, y2, . . . , yk are k linearly independent solutions on ...
 4.1.42E: Suppose that y1, y2, . . . , yk are k nontrivial solutions of a hom...
Solutions for Chapter 4.1: A First Course in Differential Equations with Modeling Applications 10th Edition
Full solutions for A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
Solutions for Chapter 4.1
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. Since 42 problems in chapter 4.1 have been answered, more than 46403 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Chapter 4.1 includes 42 full stepbystep solutions.

Acute angle
An angle whose measure is between 0° and 90°

Central angle
An angle whose vertex is the center of a circle

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

Explanatory variable
A variable that affects a response variable.

Factored form
The left side of u(v + w) = uv + uw.

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Matrix element
Any of the real numbers in a matrix

Modified boxplot
A boxplot with the outliers removed.

Periodic function
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 functions
(ƒg)(x) = ƒ(x)g(x)

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Range screen
See Viewing window.

Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

Resolving a vector
Finding the horizontal and vertical components of a vector.

Transverse axis
The line segment whose endpoints are the vertices of a hyperbola.

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

yintercept
A point that lies on both the graph and the yaxis.

zcoordinate
The directed distance from the xyplane to a point in space, or the third number in an ordered triple.