Second Order Linear Differential Equations - Pennsylvania …

2008, 2016 Zachary S Tseng B 1 1 Second Order Linear Differential Equations Second Order Linear Equations with constant coefficients; Fundamental solutions; Wronskian; Existence and Uniqueness of solutions; the characteristic equation; solutions of homogeneous Linear Equations ; reduction of Order ; Euler Equations In this chapter we will study ordinary Differential Equations of the standard form below, known as the Second Order Linear Equations : y + p(t) y + q(t) y = g(t). Homogeneous Equations : If g(t) = 0, then the equation above becomes y + p(t) y + q(t) y = 0.

The integrating factor is µ = e−5t. ( t g t dt) et( dt) et( )C Cet t u t () 5 0 5 5 1 ()= ∫µ = ∫ = = µ The actual solution y is given by the relation u = y′, and can be found by integration: 2 5 2 1 5 5 5 () e C C e C C y t =∫ ∫u t dt= Ce t dt= t + = t +. The method used in the above example can be used to solve any second

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  Methods, Factors, Integrating, Integrating factor

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