 8.8.1E: In 1–4, express a general solution to the given equation using Gaus...
 8.8.1RP: Find the first four nonzero terms in the Taylor polynomial approxim...
 8.8.1TWE: Knowing that a general solution to a nonhomogeneous linear secondo...
 8.8.2E: In 1–4, express a general solution to the given equation using Gaus...
 8.8.2RP: Determine all the singular points of the given equation and classif...
 8.8.2TWE: Discuss advantages and disadvantages of power series solutions over...
 8.8.3E: In 1–4, express a general solution to the given equation using Gaus...
 8.8.3RP: Find at least the first four nonzero terms in a power series expans...
 8.8.4E: In 1–4, express a general solution to the given equation using Gaus...
 8.8.4RP: Find a general formula for the coefficient an in a power series exp...
 8.8.5E: In 5–8, verify the following formulas by expanding each function in...
 8.8.5RP: Find at least the first four nonzero terms in a power series expans...
 8.8.6E: In 5–8, verify the following formulas by expanding each function in...
 8.8.6RP: Use the substitution y = xr to find a general solution to the given...
 8.8.7E: In 5–8, verify the following formulas by expanding each function in...
 8.8.7RP: Use the method of Frobenius to find at least the first four nonzero...
 8.8.8E: In 5–8, verify the following formulas by expanding each function in...
 8.8.8RP: Find the indicial equation and its roots and state (but do not comp...
 8.8.9E: In 9 and 10, use the method in Section 8.7 to obtain two linearly i...
 8.8.9RP: Find at least the first three nonzero terms in the series expansion...
 8.8.10E: In 9 and 10, use the method in Section 8.7 to obtain two linearly i...
 8.8.10RP: Express a general solution to the given equation using Gaussian hyp...
 8.8.11E: Show that the confluent hypergeometric equation where ? and ? are f...
 8.8.12E: Use the property of the gamma function given in (19) to derive rela...
 8.8.13E: In 13–18, express a general solution to the given equation using Be...
 8.8.14E: In 13–18, express a general solution to the given equation using Be...
 8.8.15E: In 13–18, express a general solution to the given equation using Be...
 8.8.16E: In 13–18, express a general solution to the given equation using Be...
 8.8.17E: In 13–18, express a general solution to the given equation using Be...
 8.8.18E: In 13–18, express a general solution to the given equation using Be...
 8.8.19E: In 19 and 20, a Bessel equation is given. For the appropriate choic...
 8.8.20E: In 19 and 20, a Bessel equation is given. For the appropriate choic...
 8.8.21E: Show that xvJv(x) satisfies the equation
 8.8.22E: In 22 through 24, derive the indicated recurrence formulas.Formula ...
 8.8.23E: In 22 through 24, derive the indicated recurrence formulas.Formula ...
 8.8.24E: In 22 through 24, derive the indicated recurrence formulas.Formula ...
 8.8.25E: Show that
 8.8.26E: The Bessel functions of order v = n + 1/2, n any integer, are relat...
 8.8.27E: Use Theorem 7 in Section 8.7 to determine a second linearly indepen...
 8.8.28E: Show that between two consecutive positive roots (zeros) of J1(x), ...
 8.8.29E: Use formula (43) to determine the first five Legendre polynomials.
 8.8.30E: Show that the Legendre polynomials of even degree are even function...
 8.8.31E: a) Show that the orthogonality condition (44) for Legendre polynomi...
 8.8.32E: Deduce the recurrence formula (51) for Legendre polynomials by comp...
 8.8.33E: To prove Rodrigues’s formula (52) for Legendre polynomials, complet...
 8.8.34E: Use Rodrigues’s formula (52) to obtain the representation (43) for ...
 8.8.35E: The generating function in (53) for Legendre polynomials can be der...
 8.8.36E: Find a general solution about x = 0 for the equation by first findi...
 8.8.37E: The Hermite polynomials Hn(x) are polynomial solutions to Hermite’s...
 8.8.38E: The Chebyshev (Tchebichef) polynomials Tn(x) are polynomial solutio...
 8.8.39E: The Laguerre polynomials Ln(x) are polynomial solutions to Laguerre...
Solutions for Chapter 8.8: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 8.8
Get Full SolutionsChapter 8.8 includes 51 full stepbystep solutions. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Since 51 problems in chapter 8.8 have been answered, more than 120299 students have viewed full stepbystep solutions from this chapter.

Additive identity for the complex numbers
0 + 0i is the complex number zero

Anchor
See Mathematical induction.

Circle graph
A circular graphical display of categorical data

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Degree
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

Direction angle of a vector
The angle that the vector makes with the positive xaxis

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

Ellipse
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Interquartile range
The difference between the third quartile and the first quartile.

Law of cosines
a2 = b2 + c2  2bc cos A, b2 = a2 + c2  2ac cos B, c2 = a2 + b2  2ab cos C

Length of a vector
See Magnitude of a vector.

Mean (of a set of data)
The sum of all the data divided by the total number of items

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.

Quartic regression
A procedure for fitting a quartic function to a set of data.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Solve a triangle
To find one or more unknown sides or angles of a triangle

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Unit ratio
See Conversion factor.