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# Solutions for Chapter 6.1: Solutions About Ordinary Points

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

ISBN: 9780495108368

Solutions for Chapter 6.1: Solutions About Ordinary Points

Solutions for Chapter 6.1
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##### ISBN: 9780495108368

Since 40 problems in chapter 6.1: Solutions About Ordinary Points have been answered, more than 15886 students have viewed full step-by-step solutions from this chapter. Chapter 6.1: Solutions About Ordinary Points includes 40 full step-by-step solutions. 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. Differential Equations with Boundary-Value Problems was written by and is associated to the ISBN: 9780495108368.

Key Calculus Terms and definitions covered in this textbook

If u < v , then u + w < v + w

• Characteristic polynomial of a square matrix A

det(xIn - A), where A is an n x n matrix

• Cosine

The function y = cos x

• Explanatory variable

A variable that affects a response variable.

• Graph of a polar equation

The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

• Horizontal component

See Component form of a vector.

• Intercepted arc

Arc of a circle between the initial side and terminal side of a central angle.

• Linear factorization theorem

A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ

• Mean (of a set of data)

The sum of all the data divided by the total number of items

• Midpoint (on a number line)

For the line segment with endpoints a and b, a + b2

• Numerical derivative of ƒ at a

NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002

• Odd function

A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).

• Partial fractions

The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

• Power-reducing identity

A trigonometric identity that reduces the power to which the trigonometric functions are raised.

• Quotient rule of logarithms

logb a R S b = logb R - logb S, R > 0, S > 0

• Real axis

See Complex plane.

• Reflection across the y-axis

x, y and (-x,y) are reflections of each other across the y-axis.

• Root of an equation

A solution.

• Sequence of partial sums

The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

• Solve graphically

Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

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