CONTENTS 2 2 1 Introduction SecondOrder Linear Equations

CONTENTS 2 2. 1 Introduction: Second-Order Linear Equations 2. 2 General Solutions of Linear Equations 2. 3 Homogeneous Equations with Constant Coefficients 2. 4 Mechanical Vibrations (omission) 2. 5 Nonhomogeneous Equations and Undetermined Coefficients 2. 6 Forced Oscillations and Resonance (omission) 2. 7 Electrical Circuits (omission) 2. 8 Endpoint Problems and Eigenvalues

4 二階微方標準式(Linear second-order equation) 當F(x)=0時，稱為齊性方程式 (Homogeneous equation) 當F(x)≠ 0時，稱為非齊性方程式 (nonomogeneous equation)

8 General solution For which

By 15 Solve the characteristic equation By factoring

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2. 2 線性方程式的通解 19 n-th order linear 全部除以P 0(x) (P 0(x)不等於零) 將(2)寫為齊性方程式(Homogeneous Linear equation)為：

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Recall ch 2. 1

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45 In Example 5… Polar form :

微分操作元 CHAPTER 2 Linear Equations of Higher Order 127

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