 4.7.1E: ?In 1 through 4, use Theorem 5 to discuss the existence and uniquen...
 4.7.2E: ?In 1 through 4, use Theorem 5 to discuss the existence and uniquen...
 4.7.3E: ?In 1 through 4, use Theorem 5 to discuss the existence and uniquen...
 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, ...
 4.7.9E: ?In 9 through 14, find a general solution to the given CauchyEuler...
 4.7.10E: ?In 9 through 14, find a general solution to the given CauchyEuler...
 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 CauchyEuler...
 4.7.13E: ?In 9 through 14, find a general solution to the given CauchyEuler...
 4.7.14E: ?In 9 through 14, find a general solution to the given CauchyEuler...
 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 .
 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 and , perform the following analy...
 4.7.24E: ?Solve the following CauchyEuler equations by using the substituti...
 4.7.25E: ?Let and be two functions defined on .(a) True or False: If and are...
 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 , and are solutions to the differential equation , find...
 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 general solu...
 4.7.39E: ?In 37 through 40, use variation of parameters to find general solu...
 4.7.40E: ?In 37 through 40, use variation of parameters to find general solu...
 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 Cau...
 4.7.43E: ?In 41 through 43, find general solutions to the nonhomogeneous Cau...
 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 solut...
 4.7.46E: ?In 45 through 48 , a differential equation and a nontrivial solut...
 4.7.47E: ?In 45 through 48 , a differential equation and a nontrivial solut...
 4.7.48E: ?In 45 through 48 , a differential equation and a nontrivial solut...
 4.7.49E: ?In quantum mechanics, the study of the Schrödinger equation for th...
 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 as a solution. Use the substitution to reduce thi...
 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 159270 students have viewed full stepbystep solutions from this chapter.

Circle graph
A circular graphical display of categorical data

Coefficient
The real number multiplied by the variable(s) in a polynomial term

Cone
See Right circular cone.

Cube root
nth root, where n = 3 (see Principal nth root),

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Feasible points
Points that satisfy the constraints in a linear programming problem.

Focal axis
The line through the focus and perpendicular to the directrix of a conic.

Law of sines
sin A a = sin B b = sin C c

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Pie chart
See Circle graph.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Vertical line test
A test for determining whether a graph is a function.

Ymin
The yvalue of the bottom of the viewing window.

Yscl
The scale of the tick marks on the yaxis in a viewing window.