 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 A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
Solutions for Chapter 4.1: PRELIMINARY THEORYLINEAR EQUATIONS
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. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Since 42 problems in chapter 4.1: PRELIMINARY THEORYLINEAR EQUATIONS have been answered, more than 44145 students have viewed full stepbystep solutions from this chapter. Chapter 4.1: PRELIMINARY THEORYLINEAR EQUATIONS includes 42 full stepbystep solutions.

Axis of symmetry
See Line of symmetry.

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

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Finite series
Sum of a finite number of terms.

Imaginary part of a complex number
See Complex number.

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

Inverse cotangent function
The function y = cot1 x

kth term of a sequence
The kth expression in the sequence

Measure of an angle
The number of degrees or radians in an angle

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Scalar
A real number.

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

Variable (in statistics)
A characteristic of individuals that is being identified or measured.

Vertical line
x = a.

xyplane
The points x, y, 0 in Cartesian space.

Ymax
The yvalue of the top of the viewing window.

Zero vector
The vector <0,0> or <0,0,0>.