 6.1.1: In 14 find the radius of convergence and interval of convergence fo...
 6.1.2: In 14 find the radius of convergence and interval of convergence fo...
 6.1.3: In 14 find the radius of convergence and interval of convergence fo...
 6.1.4: In 14 find the radius of convergence and interval of convergence fo...
 6.1.5: In 5 and 6 the given function is analytic at x 0. Find the first fo...
 6.1.6: In 5 and 6 the given function is analytic at x 0. Find the first fo...
 6.1.7: In 7 and 8 the given function is analytic at x 0. Find the first fo...
 6.1.8: In 7 and 8 the given function is analytic at x 0. Find the first fo...
 6.1.9: In 9 and 10 rewrite the given power series so that its general term...
 6.1.10: In 9 and 10 rewrite the given power series so that its general term...
 6.1.11: In 11 and 12 rewrite the given expression as a single power series ...
 6.1.12: In 11 and 12 rewrite the given expression as a single power series ...
 6.1.13: In 13 and 14 verify by direct substitution that the given power ser...
 6.1.14: In 13 and 14 verify by direct substitution that the given power ser...
 6.1.15: In 15 and 16 without actually solving the given differential equati...
 6.1.16: In 15 and 16 without actually solving the given differential equati...
 6.1.17: In 1728 find two power series solutions of the given differential e...
 6.1.18: In 1728 find two power series solutions of the given differential e...
 6.1.19: In 1728 find two power series solutions of the given differential e...
 6.1.20: In 1728 find two power series solutions of the given differential e...
 6.1.21: In 1728 find two power series solutions of the given differential e...
 6.1.22: In 1728 find two power series solutions of the given differential e...
 6.1.23: In 1728 find two power series solutions of the given differential e...
 6.1.24: In 1728 find two power series solutions of the given differential e...
 6.1.25: In 1728 find two power series solutions of the given differential e...
 6.1.26: In 1728 find two power series solutions of the given differential e...
 6.1.27: In 1728 find two power series solutions of the given differential e...
 6.1.28: In 1728 find two power series solutions of the given differential e...
 6.1.29: In 2932 use the power series method to solve the given initialvalu...
 6.1.30: In 2932 use the power series method to solve the given initialvalu...
 6.1.31: In 2932 use the power series method to solve the given initialvalu...
 6.1.32: In 2932 use the power series method to solve the given initialvalu...
 6.1.33: In 33 and 34 use the procedure in Example 6 to find two power serie...
 6.1.34: In 33 and 34 use the procedure in Example 6 to find two power serie...
 6.1.35: Without actually solving the differential equation (cos x)y
 6.1.36: How can the method described in this section be used to find a powe...
 6.1.37: Is x 0 an ordinary or a singular point of the differential equation xy
 6.1.38: For purposes of this problem, ignore the graphs given in Figure 6.1...
 6.1.39: (a) Find one more nonzero term for each of the solutions y1(x) and ...
 6.1.40: (a) Find one more nonzero term for each of the solutions y1(x) and ...
Solutions for Chapter 6.1: Solutions About Ordinary Points
Full solutions for Differential Equations with BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 6.1: Solutions About Ordinary Points
Get Full SolutionsSince 40 problems in chapter 6.1: Solutions About Ordinary Points have been answered, more than 15886 students have viewed full stepbystep solutions from this chapter. Chapter 6.1: Solutions About Ordinary Points includes 40 full stepbystep solutions. This textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368.

Addition property of inequality
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.

Powerreducing 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 yaxis
x, y and (x,y) are reflections of each other across the yaxis.

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