 4.1.1: In 14 the given family of functions is the general solution of the ...
 4.1.2: In 14 the given family of functions is the general solution of the ...
 4.1.3: In 14 the given family of functions is the general solution of the ...
 4.1.4: In 14 the given family of functions is the general solution of the ...
 4.1.5: Given that y c1 c2x2 is a twoparameter family of solutions of xy y...
 4.1.6: Find two members of the family of solutions in that satisfy the ini...
 4.1.7: Given that x(t) c1 cos vt c2 sin vt is the general solution of x v2...
 4.1.8: Use the general solution of x v2x 0 given in to show that a solutio...
 4.1.9: In 9 and 10 find an interval centered about x 0 for which the given...
 4.1.10: In 9 and 10 find an interval centered about x 0 for which the given...
 4.1.11: (a) Use the family in to find a solution of y y 0 that satisfies th...
 4.1.12: Use the family in to find a solution of xy y 0 that satisfies the b...
 4.1.13: In 13 and 14 the given twoparameter family is a solution of the in...
 4.1.14: In 13 and 14 the given twoparameter family is a solution of the in...
 4.1.15: In 1522 determine whether the given set of functions is linearly in...
 4.1.16: In 1522 determine whether the given set of functions is linearly in...
 4.1.17: In 1522 determine whether the given set of functions is linearly in...
 4.1.18: In 1522 determine whether the given set of functions is linearly in...
 4.1.19: In 1522 determine whether the given set of functions is linearly in...
 4.1.20: In 1522 determine whether the given set of functions is linearly in...
 4.1.21: In 1522 determine whether the given set of functions is linearly in...
 4.1.22: In 1522 determine whether the given set of functions is linearly in...
 4.1.23: In 2330 verify that the given functions form a fundamental set of s...
 4.1.24: In 2330 verify that the given functions form a fundamental set of s...
 4.1.25: In 2330 verify that the given functions form a fundamental set of s...
 4.1.26: In 2330 verify that the given functions form a fundamental set of s...
 4.1.27: In 2330 verify that the given functions form a fundamental set of s...
 4.1.28: In 2330 verify that the given functions form a fundamental set of s...
 4.1.29: In 2330 verify that the given functions form a fundamental set of s...
 4.1.30: In 2330 verify that the given functions form a fundamental set of s...
 4.1.31: In 3134 verify that the given twoparameter family of functions is ...
 4.1.32: In 3134 verify that the given twoparameter family of functions is ...
 4.1.33: In 3134 verify that the given twoparameter family of functions is ...
 4.1.34: In 3134 verify that the given twoparameter family of functions is ...
 4.1.35: (a) Verify that and are, respectively, particular solutions of and ...
 4.1.36: (a) By inspection find a particular solution of y 2y 10. (b) By ins...
 4.1.37: Let n 1, 2, 3, . . . . Discuss how the observations Dn x n1 0 and D...
 4.1.38: Suppose that y1 ex and y2 ex are two solutions of a homogeneous lin...
 4.1.39: (a) Verify that y1 x3 and y2 x 3 are linearly independent solutions...
 4.1.40: Is the set of functions f1(x) ex2 , f2(x) ex3 linearly dependent or...
 4.1.41: Suppose y1, y2, . . . , yk are k linearly independent solutions on ...
 4.1.42: Suppose that y1, y2, . . . , yk are k nontrivial solutions of a hom...
Solutions for Chapter 4.1: Preliminary TheoryLinear Equations
Full solutions for Differential Equations with BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 4.1: Preliminary TheoryLinear Equations
Get Full SolutionsThis textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems, edition: 7. Chapter 4.1: Preliminary TheoryLinear Equations includes 42 full stepbystep solutions. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368. Since 42 problems in chapter 4.1: Preliminary TheoryLinear Equations have been answered, more than 16871 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Annuity
A sequence of equal periodic payments.

Dihedral angle
An angle formed by two intersecting planes,

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Eccentricity
A nonnegative number that specifies how offcenter the focus of a conic is

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Future value of an annuity
The net amount of money returned from an annuity.

Halfangle identity
Identity involving a trigonometric function of u/2.

Identity
An equation that is always true throughout its domain.

Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Permutation
An arrangement of elements of a set, in which order is important.

Probability function
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.

Radicand
See Radical.

Range screen
See Viewing window.

Response variable
A variable that is affected by an explanatory variable.

Terms of a sequence
The range elements of a sequence.

Xmin
The xvalue of the left side of the viewing window,.