Chapter 18: Elementary Differential Equations Bernoulli Equations: Homogeneous Equations; Numerical Methods (18.2.1), Bernoulli equation, pp. 1099, 1100 Homogeneous equations, p. 1101 Euler method, p. 1104, figure 18.2.2 Runge-Kutta method, p. 1105 Exact Equations Exact differential equation, (18.3.1), p. 1108 (18.3.2), p. 1111 (18.3.3), p. 1112   The Equation y”+ay’+by=0 (18.4.1), p. 1113 Characteristic equation pp. 1113, 1114 Existence and uniqueness theorem, p. 1115 Wronskian, p. 1116 Theorem 18.4.4, p. 1116 Theorem 18.4.5, p. 1117 Theorem 18.4.6, p. 1118 The Equation y”+ay’+by=(x) The complete equation, (18.5.1), p. 1123 (18.5.2), p. 1123 (18.5.3), p. 1123 (18.5.4), p. 1123 Variation of parameters, (18.5.6), p. 1125 Mechanical Vibrations Simple harmonic motion, (18.6.1), p. 1130 General solution, (18.6.2), p. 1131 Period, frequency, amplitude, phase shift, p. 1131 Figure 18.6.1, p. 1131 Damped vibrations, (18.6.3), p. 1134 Underdamped, overdamped, critically damped, (18.6.4-6), p. 1135 Forced vibrations, (18.6.7-8), p. 1136 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Bernoulli Equations: Homogeneous Equations; Numerical Methods (18.2.1), Bernoulli equations, pp. 1099, 1100 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Bernoulli Equations: Homogeneous Equations; Numerical Methods Homogeneous equations, p. 1101 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Bernoulli Equations: Homogeneous Equations; Numerical Methods Euler method, p. 1104, figure 18.2.2 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Bernoulli Equations: Homogeneous Equations; Numerical Methods Runge-Kutta method, p. 1105 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Exact Equations Exact differential equation, (18.3.1), p. 1108 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Exact Equations (18.3.2), p. 1111 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Exact Equations (18.3.3), p. 1112 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=0 (18.4.1), p. 1113 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=0 Characteristics equation pp. 1113, 1114 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=0 Existence and uniqueness theorem, p. 1115 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=0 Wronskian, p. 1116 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=0 Theorem 18.4.4, p. 1116 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=0 Theorem 18.4.5, p. 1117 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=0 Theorem 18.4.6, p. 1118 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=φ(x) The complete equation, (18.5.1), p. 1123 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=φ(x) (18.5.2), p. 1123 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=φ(x) (18.5.3), p. 1123 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=φ(x) (18.5.4), p. 1123 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

The Equation y”+ay’+by=φ(x) Variation of parameters, (18.5.6), p. 1125 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Mechanical Vibrations Simple harmonic motion, (18.6.1), p. 1130 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Mechanical Vibrations General solution, (18.6.2), p. 1131 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Mechanical Vibrations Period, frequency, amplitude, phase shift, p. 1131 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Mechanical Vibrations Figure 18.6.1. p. 1131 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Mechanical Vibrations Damped vibrations, (18.6.3), p. 1134 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Mechanical Vibrations Underdamped, overdamped, critically damped, (18.6.4-6), p. 1135 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.

Mechanical Vibrations Forced vibrations, (18.6.7-8), p. 1136 Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved.