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

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online