 6.4.1: In 16 use (1) to find the general solution of the given differentia...
 6.4.2: In 16 use (1) to find the general solution of the given differentia...
 6.4.3: In 16 use (1) to find the general solution of the given differentia...
 6.4.4: In 16 use (1) to find the general solution of the given differentia...
 6.4.5: In 16 use (1) to find the general solution of the given differentia...
 6.4.6: In 16 use (1) to find the general solution of the given differentia...
 6.4.7: In 710 use (12) to find the general solution of the given different...
 6.4.8: In 710 use (12) to find the general solution of the given different...
 6.4.9: In 710 use (12) to find the general solution of the given different...
 6.4.10: In 710 use (12) to find the general solution of the given different...
 6.4.11: In 11 and 12 use the indicated change of variable to find the gener...
 6.4.12: In 11 and 12 use the indicated change of variable to find the gener...
 6.4.13: In 1320 use (18) to find the general solution of the given differen...
 6.4.14: In 1320 use (18) to find the general solution of the given differen...
 6.4.15: In 1320 use (18) to find the general solution of the given differen...
 6.4.16: In 1320 use (18) to find the general solution of the given differen...
 6.4.17: In 1320 use (18) to find the general solution of the given differen...
 6.4.18: In 1320 use (18) to find the general solution of the given differen...
 6.4.19: In 1320 use (18) to find the general solution of the given differen...
 6.4.20: In 1320 use (18) to find the general solution of the given differen...
 6.4.21: Use the series in (7) to verify that I (x) i J (ix) is a real funct...
 6.4.22: Assume that b in equation (18) can be pure imaginary, that is, b i,...
 6.4.23: In 2326 first use (18) to express the general solution of the given...
 6.4.24: In 2326 first use (18) to express the general solution of the given...
 6.4.25: In 2326 first use (18) to express the general solution of the given...
 6.4.26: In 2326 first use (18) to express the general solution of the given...
 6.4.27: (a) Proceed as in Example 5 to show that xJ (x) J(x) xJ1(x). [Hint:...
 6.4.28: Use the formula obtained in Example 5 along with part (a) of to der...
 6.4.29: In 29 and 30 use (20) or (21) to obtain the given result.
 6.4.30: In 29 and 30 use (20) or (21) to obtain the given result.
 6.4.31: Proceed as on page 264 to derive the elementary form of J1/2(x) giv...
 6.4.32: Use the recurrence relation in along with (23) and (24) to express ...
 6.4.33: Use the change of variables to show that the differential equation ...
 6.4.34: Show that is a solution of Airys differential equation y 2xy 0, x 0...
 6.4.35: (a) Use the result of to express the general solution of Airys diff...
 6.4.36: Use the Table 6.4.1 to find the first three positive eigenvalues an...
 6.4.37: (a) Use (18) to show that the general solution of the differential ...
 6.4.38: Use a CAS to graph J3/2(x), J3/2(x), J5/2(x), and J5/2(x).
 6.4.39: (a) Use the general solution given in Example 4 to solve the IVP Al...
 6.4.40: (a) Use the general solution obtained in to solve the IVP Use a CAS...
 6.4.41: A uniform end embedded in the ground, will deflect, or bend away, f...
 6.4.42: For the simple pendulum described on page 220 of Section 5.3, suppo...
 6.4.43: (a) Use the explicit solutions y1(x) and y2(x) of Legendres equatio...
 6.4.44: Use the recurrence relation (32) and P0(x) 1, P1(x) x, to generate ...
 6.4.45: Use the recurrence relation (32) and P0(x) 1, P1(x) x, to generate ...
 6.4.46: Show that the differential equation can be transformed into Legendr...
 6.4.47: Find the first three positive values of for which the problem has n...
 6.4.48: For purposes of this problem ignore the list of Legendre polynomial...
 6.4.49: Use a CAS to graph P1(x), P2(x), . . . , P7 (x) on the interval [1,...
 6.4.50: Use a rootfindin application to fin the zeros of P1(x), P2(x), . ....
 6.4.51: The differential equation y 2xy 2ay 0 y
 6.4.52: (a) When is a nonnegative integer, Hermites differential equation a...
 6.4.53: The differential equation , where is a parameter, is known as Cheby...
 6.4.54: If n is an integer, use the substitution to show that the general s...
Solutions for Chapter 6.4: SPECIAL FUNCTIONS
Full solutions for A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
Solutions for Chapter 6.4: SPECIAL FUNCTIONS
Get Full SolutionsSince 54 problems in chapter 6.4: SPECIAL FUNCTIONS have been answered, more than 44176 students have viewed full stepbystep solutions from this chapter. 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. Chapter 6.4: SPECIAL FUNCTIONS includes 54 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Elements of a matrix
See Matrix element.

End behavior
The behavior of a graph of a function as.

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Equivalent vectors
Vectors with the same magnitude and direction.

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

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

Orthogonal vectors
Two vectors u and v with u x v = 0.

Parametrization
A set of parametric equations for a curve.

Perihelion
The closest point to the Sun in a planet’s orbit.

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Quadratic regression
A procedure for fitting a quadratic function to a set of data.

Randomization
The principle of experimental design that makes it possible to use the laws of probability when making inferences.

Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j