 4.7.1E: In the Problem, use Theorem 5 to discuss the existence and uniquene...
 4.7.2E: In the Problem, use Theorem 5 to discuss the existence and uniquene...
 4.7.3E: In the Problem, use Theorem 5 to discuss the existence and uniquene...
 4.7.4E: In 1 through 4, use Theorem 5 to discuss the existence and uniquene...
 4.7.5E: In 5 through 8, determine whether Theorem 5 applies. If it does, th...
 4.7.6E: In 5 through 8, determine whether Theorem 5 applies. If it does, th...
 4.7.7E: In 5 through 8, determine whether Theorem 5 applies. If it does, th...
 4.7.8E: In 5 through 8, determine whether Theorem 5 applies. If it does, th...
 4.7.9E: In 9 through 14, find a general solution to the given Cauchy–Euler ...
 4.7.10E: In 9 through 14, find a general solution to the given Cauchy–Euler ...
 4.7.11E: In 9 through 14, find a general solution to the given Cauchy–Euler ...
 4.7.12E: In 9 through 14, find a general solution to the given Cauchy–Euler ...
 4.7.13E: In 9 through 14, find a general solution to the given Cauchy–Euler ...
 4.7.14E: In 9 through 14, find a general solution to the given Cauchy–Euler ...
 4.7.15E: In 15 through 18, find a general solution for t < 0.
 4.7.16E: In 15 through 18, find a general solution for t < 0.
 4.7.17E: In 15 through 18, find a general solution for t < 0.
 4.7.18E: In 15 through 18, find a general solution for t < 0.
 4.7.19E: In 19 and 20, solve the given initial value problem for the Cauchy–...
 4.7.20E: In 19 and 20, solve the given initial value problem for the Cauchy–...
 4.7.21E: In 21 and 22, devise a modification of the method for Cauchy–Euler ...
 4.7.22E: In 21 and 22, devise a modification of the method for Cauchy–Euler ...
 4.7.23E: To justify the solution formulas (8) and (9), perform the following...
 4.7.24E: Solve the following Cauchy–Euler equations by using the substitutio...
 4.7.25E: Let y1 and y2 be two functions defined on (a) True or False: If y1 ...
 4.7.26E: Let Are y1 and y2 linearly independent on the following intervals?(...
 4.7.27E: Consider the linear equation (21) (a) verify that y1(t) : =t and y2...
 4.7.28E: Let y1(t) = t2 and y2(t) = 2tt. Are y1 and y2 linearly independen...
 4.7.29E: Prove that if y1 and y2 are linearly independent solutions Of on (a...
 4.7.30E: Superposition Principle. Let y1 be a solution to on the interval I ...
 4.7.31E: Determine whether the following functions can be Wronskians on 1 <...
 4.7.32E: By completing the following steps, prove that the Wronskian of any ...
 4.7.33E: Use Abel’s formula ( 32) to determine (up to a constant multiple) t...
 4.7.34E: All that is known concerning a mysterious differential equation is ...
 4.7.35E: Given that 1+t,1+2t,and 1+3t2 are solutions to the differential equ...
 4.7.36E: Verify that the given functions y1 and y2 are linearly independent ...
 4.7.37E: In 37 through 40, use variation of parameters to find a general sol...
 4.7.38E: In 37 through 40, use variation of parameters to find a general sol...
 4.7.39E: In 37 through 40, use variation of parameters to find a general sol...
 4.7.40E: In 37 through 40, use variation of parameters to find a general sol...
 4.7.41E: In 41 through 43, find general solutions to the nonhomogeneous Cauc...
 4.7.42E: In 41 through 43, find general solutions to the nonhomogeneous Cauc...
 4.7.43E: In 41 through 43, find general solutions to the nonhomogeneous Cauc...
 4.7.44E: The Bessel equation of order onehalf has two linearly independent ...
 4.7.45E: In 45 through 48, a differential equation and a nontrivial solutio...
 4.7.46E: In 45 through 48, a differential equation and a nontrivial solutio...
 4.7.47E: In 45 through 48, a differential equation and a nontrivial solutio...
 4.7.48E: In 45 through 48, a differential equation and a nontrivial solutio...
 4.7.49E: In quantum mechanics, the study of the Schrödinger equation for the...
 4.7.50E: Complete the proof of Theorem 8 by solving equation (16).Theorem 8....
 4.7.51E: The reduction of order procedure can be used more generally to redu...
 4.7.52E: The equation Has f(t) =t as a solution. Use the substitution y(t) =...
 4.7.53E: Isolated Zeros. Let ?(t) be a solution to y’’+py’+qy = 0 on (a, b),...
 4.7.54E: The reduction of order formula (13) can also be derived from Abels’...
Solutions for Chapter 4.7: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 4.7
Get Full SolutionsFundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. Chapter 4.7 includes 54 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since 54 problems in chapter 4.7 have been answered, more than 66508 students have viewed full stepbystep solutions from this chapter.

Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Cosecant
The function y = csc x

Halfangle identity
Identity involving a trigonometric function of u/2.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Length of a vector
See Magnitude of a vector.

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Maximum rvalue
The value of r at the point on the graph of a polar equation that has the maximum distance from the pole

Minor axis
The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

Multiplication property of equality
If u = v and w = z, then uw = vz

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Relation
A set of ordered pairs of real numbers.

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.

Vertex form for a quadratic function
ƒ(x) = a(x  h)2 + k

Vertical translation
A shift of a graph up or down.

yzplane
The points (0, y, z) in Cartesian space.