 6.4.1E: In 1–6 use (1) to find the general solution of the given differenti...
 6.4.2E: In 1–6 use (1) to find the general solution of the given differenti...
 6.4.3E: In 1–6 use (1) to find the general solution of the given differenti...
 6.4.4E: In 1–6 use (1) to find the general solution of the given differenti...
 6.4.5E: In 1–6 use (1) to find the general solution of the given differenti...
 6.4.6E: In 1–6 use (1) to find the general solution of the given differenti...
 6.4.7E: In 7–10 use (12) to find the general solution of the given differen...
 6.4.8E: In 7–10 use (12) to find the general solution of the given differen...
 6.4.9E: In 7–10 use (12) to find the general solution of the given differen...
 6.4.10E: In 7–10 use (12) to find the general solution of the given differen...
 6.4.11E: In 11 and 12 use the indicated change of variable to find the gener...
 6.4.12E: In 11 and 12 use the indicated change of variable to find the gener...
 6.4.13E: In 13–20 use (18) to find the general solution of the given differe...
 6.4.14E: In 13–20 use (18) to find the general solution of the given differe...
 6.4.15E: In 13–20 use (18) to find the general solution of the given differe...
 6.4.16E: In 13–20 use (18) to find the general solution of the given differe...
 6.4.17E: In 13–20 use (18) to find the general solution of the given differe...
 6.4.18E: In 13–20 use (18) to find the general solution of the given differe...
 6.4.19E: In 13–20 use (18) to find the general solution of the given differe...
 6.4.20E: In 13–20 use (18) to find the general solution of the given differe...
 6.4.21E: Use the series in (7) to verify that is a real function.Reference :...
 6.4.22E: Assume that b in equation (18) can be pure imaginary, that is, Use ...
 6.4.23E: In 23–26 first use (18) to express the general solution of the give...
 6.4.24E: In 23–26 first use (18) to express the general solution of the give...
 6.4.25E: In 23–26 first use (18) to express the general solution of the give...
 6.4.26E: In 23–26 first use (18) to express the general solution of the give...
 6.4.27E: (a) Proceed as in Example 5 to show that (b) Use the result in part...
 6.4.28E: Use the formula obtained in Example 5 along with part (a) of to der...
 6.4.29E: In 29 and 30 use (20) or (21) to obtain the given result. Reference...
 6.4.30E: In 29 and 30 use (20) or (21) to obtain the given result. Reference...
 6.4.31E: Proceed as on page 247 to derive the elementary form of J1/2(x) gi...
 6.4.32E: Use the recurrence relation in along with (23) and (24) to express ...
 6.4.33E:
 6.4.34E:
 6.4.35E: (a) Use the result of to express the general solution of Airy’s dif...
 6.4.36E: Use the Table 6.1 to find the first three positive eigenvalues and ...
 6.4.37E: (a) Use (18) to show that the general solution of the differential ...
 6.4.38E: Use a CAS to graph and
 6.4.39E: (a) Use the general solution given in Example 4 to solve the IVP Al...
 6.4.40E: (a) Use the general solution obtained in to solve the IVP Use a CAS...
 6.4.41E: Column Bending Under Its Own Weight A uniform thin column of length...
 6.4.42E: Buckling of a Thin Vertical Column In Example 3 of Section 5.2 we s...
 6.4.43E: Pendulum of Varying Length For the simple pendulum described on pag...
 6.4.44E: (a) Use the explicit solutions y1(x) and y2(x) of Legendre’s equati...
 6.4.45E: Use the recurrence relation (29) and P0(x) = 1, P1(x) = x, to gener...
 6.4.46E: Show that the differential equation can be transformed into Legendr...
 6.4.47E: Find the first three positive values of for which the problem has n...
 6.4.48E: For purposes of this problem ignore the list of Legendre polynomial...
 6.4.49E: Use a CAS to graph P1(x), P2(x), . . . , P7 (x) on the interval [?1...
 6.4.50E: Use a rootfinding application to find the zeros of P1(x), P2(x), ....
 6.4.51E: The differential equation is known as Hermite’s equation of order _...
 6.4.52E: (a) When is a nonnegative integer, Hermite’s differential equation ...
 6.4.53E: The differential equation where is a parameter, is known as Chebysh...
 6.4.54E: If n is an integer, use the substitution to show that the general s...
Solutions for Chapter 6.4: A First Course in Differential Equations with Modeling Applications 10th Edition
Full solutions for A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
Solutions for Chapter 6.4
Get Full SolutionsSince 54 problems in chapter 6.4 have been answered, more than 44395 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. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6.4 includes 54 full stepbystep solutions.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Compound interest
Interest that becomes part of the investment

Compounded monthly
See Compounded k times per year.

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)

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Exponential function
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

Factored form
The left side of u(v + w) = uv + uw.

Fibonacci numbers
The terms of the Fibonacci sequence.

Graphical model
A visible representation of a numerical or algebraic model.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Monomial function
A polynomial with exactly one term.

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

Normal distribution
A distribution of data shaped like the normal curve.

Phase shift
See Sinusoid.

Regression model
An equation found by regression and which can be used to predict unknown values.

Solve by substitution
Method for solving systems of linear equations.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.