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# Solutions for Chapter 4.7: Cauchy-Euler Equation

## Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition

ISBN: 9780495108368

Solutions for Chapter 4.7: Cauchy-Euler Equation

Solutions for Chapter 4.7
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##### ISBN: 9780495108368

Differential Equations with Boundary-Value Problems was written by and is associated to the ISBN: 9780495108368. Since 47 problems in chapter 4.7: Cauchy-Euler Equation have been answered, more than 17028 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Differential Equations with Boundary-Value Problems, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.7: Cauchy-Euler Equation includes 47 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a complex number

The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

• Angle between vectors

The angle formed by two nonzero vectors sharing a common initial point

• Aphelion

The farthest point from the Sun in a planet’s orbit

• Circle

A set of points in a plane equally distant from a fixed point called the center

• Decreasing on an interval

A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

• 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

• equation of a hyperbola

(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1

• Finite series

Sum of a finite number of terms.

• 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.

• Magnitude of a vector

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

• Mathematical induction

A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

• Multiplicative inverse of a complex number

The reciprocal of a + bi, or 1 a + bi = a a2 + b2- ba2 + b2 i

• Positive numbers

Real numbers shown to the right of the origin on a number line.

• Quartic function

A degree 4 polynomial function.

• Relation

A set of ordered pairs of real numbers.

• Secant

The function y = sec x.

• Solution set of an inequality

The set of all solutions of an inequality

• Sum of complex numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

• Terms of a sequence

The range elements of a sequence.

• Variable

A letter that represents an unspecified number.