Fyrilestrar+STAE+III+verkfraedi+-+skammtur+4

2aex axex 2aex 2axex 3axex 8ex 4aex 8ex yp

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Unformatted text preview: )T y2 (∗∗) ￿ y1 y2 , ￿ ￿ y1 y2 z = Y v, T v = (u, v ) u v p = v(x) Y ￿ p = AY p x x z￿ = Y ￿ v + Y v￿ = AY v + Y v￿ = Az + Y v￿ . z (∗∗) ￿￿ 0 z = Az + Y v = Az + , f ￿! ￿ ￿￿ 0 Yv = . f ￿ x u ￿ y1 + v ￿ y2 = 0 Y (x) ￿ ￿ u￿ y1 + v ￿ y2 = f. y ￿￿ + p(x)y ￿ + q (x)y = f (x). p(x) q (x) p(x) = A q (x) = B f (x) y ￿￿ − 4y = 8x2 − 2x. yp (x) ab ￿ yp (x) = 2ax + b ￿￿ yp (x) = 2a. ! 2a − 4(ax2 + bx + c) = 8x2 − 2x, yp (x) = ax2 + bx + c c p −4ax2 − 4bx + 2a − 4c = 8x2 − 2x. b = 1/2 c = −1 −4a = 8 −4b = −2 2a − 4c = 0 a = −2 1 yp (x) = −2x2 + x − 1. 2 y ￿￿ − 4y = 0. z2 − 4 −2 y1 (x) = e−2x 2 y2 (x) = e2x 1 y (x) = c1 e−2x + c2 e2x − 2x2 + x − 1. 2 ✷ y ￿￿ − 5y ￿ + 6y = −3...
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This document was uploaded on 02/16/2014.

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