Transcription of Second Order Linear Differential Equations
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Second Order Linear Differential Equations
CHAPTER 3 Second Order Linear Differential Introduction; Basic Terminology and ResultsAny Second Order differential equation can be written asF(x,y,y ,y )=0 This chapter is concerned with special yet very important Second Order Equations , namelylinear that a first Order Linear differential equation is an equation which can be writtenin the formy +p(x)y=q(x)wherepandqare continuous functions on some intervalI. A Second Order , lineardifferential equation has an analogous Order Linear differential equationis an equation which canbe written in the formy +p(x)y +q(x)y=f(x)(1)wherep, q, andfare continuous functions on some functionspandqare called thecoefficientsof the equation; the functionfonthe right-hand side is called theforcing functionor thenonhomogeneous term. The term forcing function comes from applications of Second - Order Linear Equations ; the description nonhomogeneous is given Second Order equation which is not Linear is said to (a)y 5y +6y= 3cos2x.
(c) y00 +xy2y0 −y3 = exy is a nonlinear equation; this equation cannot be written in the form (1). Remarks on “Linear.” Intuitively, a second order differential equation is linear if y00 appears in the equation with exponent 1 only, and if either or both of y and y0 appear in the equation, then they do so with exponent 1 only.
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