 7.9.1E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.1RP: In 1 and 2, use the definition of the Laplace transform to determine
 7.9.1TWE: Compare the use of Laplace transforms in solving linear differentia...
 7.9.2E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.2RP: In 1 and 2, use the definition of the Laplace transform to determine
 7.9.2TWE: Explain why the method of Laplace transforms works so well for line...
 7.9.3E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.3TWE: Discuss several examples of initial value problems in which the met...
 7.9.4E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.4RP: In 3–10, determine the Laplace transform of the given function.
 7.9.4TWE: A linear system is said to be asymptotically stable if its impulse ...
 7.9.5E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.5RP: In 3–10, determine the Laplace transform of the given function.
 7.9.5TWE: Compare and contrast the solution of initial value problems by Lapl...
 7.9.6E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.6RP: In 3–10, determine the Laplace transform of the given function.
 7.9.7E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.7RP: In 3–10, determine the Laplace transform of the given f unction. t ...
 7.9.8E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.8RP: In 3–10, determine the Laplace transform of the given function.
 7.9.9E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.9RP: In 3–10, determine the Laplace transform of the given function.
 7.9.10E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.10RP: In 3–10, determine the Laplace transform of the given function.
 7.9.11E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.11RP: In 11–17, determine the inverse Laplace transform of the given func...
 7.9.12E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.12RP: In 11–17, determine the inverse Laplace transform of the given func...
 7.9.13E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.13RP: In 11–17, determine the inverse Laplace transform of the given func...
 7.9.14E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.14RP: In 11–17, determine the inverse Laplace transform of the given func...
 7.9.15E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.15RP: In 11–17, determine the inverse Laplace transform of the given func...
 7.9.16E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.16RP: In 11–17, determine the inverse Laplace transform of the given func...
 7.9.17E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.17RP: In 11–17, determine the inverse Laplace transform of the given func...
 7.9.18E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.18RP: Find the Taylor series for f(t) = et2 about t = 0. Then, assuming ...
 7.9.19E: In 1–19, use the method of Laplace transforms to solve the given in...
 7.9.19RP: In 19–24, solve the given initial value problem for y(t) using the ...
 7.9.20E: Use the method of Laplace transforms to solve [Hint:y(0) = c Let an...
 7.9.20RP: In 19–24, solve the given initial value problem for y(t) using the ...
 7.9.21RP: In 19–24, solve the given initial value problem for y(t) using the ...
 7.9.22E: Recompute the coupled mass–spring oscillator motion in 1, Exercises...
 7.9.22RP: In 19–24, solve the given initial value problem for y(t) using the ...
 7.9.23E: In 23 and 24, find a system of differential equations and initial c...
 7.9.23RP: In 19–24, solve the given initial value problem for y(t) using the ...
 7.9.24E: In 23 and 24, find a system of differential equations and initial c...
 7.9.24RP: In 19–24, solve the given initial value problem for y(t) using the ...
 7.9.25RP: In 25 and 26, find solutions to the given initial value problem.
 7.9.26RP: In 25 and 26, find solutions to the given initial value problem.
 7.9.27RP: In 27 and 28, solve the given equation for y(t).
 7.9.28RP: In 27 and 28, solve the given equation for y(t).
 7.9.29RP: A linear system is governed by Find the transfer function and the i...
 7.9.30RP: Solve the symbolic initial value problem
 7.9.31RP: In 31 and 32, use Laplace transforms to solve the given system.
 7.9.32RP: In 31 and 32, use Laplace transforms to solve the given system.
Solutions for Chapter 7.9: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations  8th Edition
ISBN: 9780321747730
Solutions for Chapter 7.9
Get Full SolutionsThis 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 59 problems in chapter 7.9 have been answered, more than 56668 students have viewed full stepbystep solutions from this chapter. Chapter 7.9 includes 59 full stepbystep solutions. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730.

Axis of symmetry
See Line of symmetry.

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

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Cubic
A degree 3 polynomial function

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

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

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Length of a vector
See Magnitude of a vector.

Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers

Logistic regression
A procedure for fitting a logistic curve to a set of data

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

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

Pie chart
See Circle graph.

Product of complex numbers
(a + bi)(c + di) = (ac  bd) + (ad + bc)i

Quadrantal angle
An angle in standard position whose terminal side lies on an axis.

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

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

Vertices of an ellipse
The points where the ellipse intersects its focal axis.