Transcription of HIGHER-ORDER DIFFERENTIAL EQUATIONS
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HIGHER-ORDER DIFFERENTIAL EQUATIONS
HIGHER-ORDER . DIFFERENTIAL EQUATIONS 3. Chapter Contents Theory of Linear EQUATIONS Initial-Value and Boundary-Value Problems homogeneous EQUATIONS Nonhomogeneous EQUATIONS Reduction of Order homogeneous Linear EQUATIONS with Constant Coefficients Undetermined Coefficients Variation of Parameters Cauchy Euler Equation Nonlinear EQUATIONS Linear Models: Initial-Value Problems Spring/Mass Systems: Free Undamped Motion Spring/Mass Systems: Free Damped Motion Spring/Mass Systems: Driven Motion Series Circuit Analogue Linear Models: Boundary-Value Problems Green's Functions Initial-Value Problems Boundary-Value Problems Nonlinear Models Solving Systems of Linear EQUATIONS Chapter 3 in Review We turn now to DEs of order two and higher. In the first six sections of this chapter we examine some of the underlying theory of linear DEs and meth- ods for solving certain kinds of linear EQUATIONS . The difficulties that surround HIGHER-ORDER nonlinear DEs and the few methods that yield analytic solutions of such EQUATIONS are examined next (Section ).
3.1.2 Homogeneous Equations A linear nth-order differential equation of the form a n1x2 d ny dx n 1 a n211x2 d n21y dxn21 1 p1 a 11x2 dy dx 1 a 01x2y 0 solution of a homogeneous (6) is said to be homogeneous, whereas an equation a n1x2 d ny dxn 1 a n211x2 d n21y dxn21 1 p1 a 11x2 dy dx 1 a 01x2y g1x2 (7) with g(x) not identically zero, is said ...
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