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# Y2 py2 qy2 0 u y1 2u y1 uy1 p u y1

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Unformatted text preview: ￿ ￿ (ϕ−yp )￿￿ +p(x)·(ϕ−yp )￿ +q (x)·(ϕ−yp ) = ϕ￿￿ +p(x)ϕ￿ +q (x)ϕ− yp + p(x)yp + q (x)yp = f (x)−f (x) = 0 c1 c2 ϕ(x) − yp (x) = c1 · y1 (x) + c2 · y2 (x) ϕ(x) = yp (x) + c1 · y1 (x) + c2 · y2 (x). y ￿￿ + p(x)y ￿ + q (x)y = f (x) y1 (x) y2 (x) y ￿￿ + p(x)y ￿ + q (x)y = 0 ✷ yp (x) y ￿￿ + p(x)y ￿ + q (x)y = f (x). y (x) = c1 · y1 (x) + c2 · y2 (x) + yp (x), c1 c2 y ￿￿ + p(x)y ￿ + q (x)y = 0 y1 ￿= 0 y ￿￿ + p(x)y ￿ + q (x)y = 0, y2 (x) = u(x) · y1 (x) ￿ ￿ y2 = u￿ y1 + uy1 u(x) y2 (x) ￿￿ ￿ ￿ ￿￿ ￿ ￿￿ y2 = u￿￿ y1 + u￿ y1 + u￿ y1 + uy1 = u￿￿ y1 + 2u￿ y1 + uy1 y2 ! ￿￿ ￿ y2 + py2 + qy2 = 0, ! ￿ ￿￿ ￿ u￿￿ y1 + 2u￿ y1 + uy1 + p · (u￿ y1 + uy1 ) + quy1 = 0, ! ￿ ￿￿ ￿ u￿￿ y1 + u￿ [2y1 + py1 ] + u[y1 + py1 + qy1 ] = 0. y1 ￿￿ ￿ y1 + py1 + qy1 = 0 ! ￿ u￿￿ y1 + u￿ [2y1 + py1 ] = 0, u￿￿ + g (x)u￿ = 0 g (x) = y1 (x) ￿= 0 ￿ 2y1 (x) + p(x)y1 (x) , y1 (x) v = u￿ v ￿ + g (x)v = 0 G(x) g (x) v (x) = e−G(x) u(x) = ￿ e−G(x) dx y2 (x) = u(x) · y1 (x) y ￿￿ + p(x)y ￿ + q (x)y = 0. ￿ ￿ ￿ ￿ W (x) = y1 y2 − y1 y2 = y1 (u￿ y1 + uy1 ) − y1 u...
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## This document was uploaded on 02/16/2014.

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