ch03 - Chapter Review Sheets for Elementary Differential...

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Chapter Review Sheets for Elementary Differential Equations and Boundary Value Problems, 8e Chapter 3: Second Order Linear Equations Definitions: Linear and nonlinear Homogeneous, Nonhomogeneous Characteristic Equation Wronskian General Solution, Fundamental Set of Solutions Principle of superposition (p. 145) Linear Independence Particular Solution Method of undetermined solutions Period, Natural Frequency, Amplitude, Phase Overdamped, Critically Damped, Underdamped Resonance Transient Solution, Steady-State Solution or Forced Response Theorems: Theorem 3.2.1: Existence and uniqueness of solutions to )'"+ p(l) y.+q(t)y ~ g(t) Y(to) = Ya Y"(to } = Yo Theorem 3.2.2: Principle of superposition. If Yi and Y2 are solutions to so is C, Y, + c2 Y2 for any constants c' and c2 . Theorem 3.2.3: Finding solutions to Eq. (2) an Eq. (3), using the Wronskian at the initial conditions. Theorem 3.2.4: Representing general solutions to second order linear homogeneous GDE's Theorem 3.2.5: Existence of a fundamental set of solutions. Theorem 3.3.1: Linear independence of functions and the Wronskian.
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