Lecture 5 Notes

# For the equation y 4y 4y 0 say you know guess y2

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Unformatted text preview: = 4v ￿ (t)e−2t − 8v (t)e−2t ￿￿ y2 (t) = v ￿￿ (t)e−2t − 2v ￿ (t)e−2t − 2v ￿ (t)e−2t + 4v (t)e−2t ￿￿ ￿ y 2 + 4y2 + 4y2 = Reduction of order y1 (t) = e−2t . For the equation y + 4y + 4y = 0 , say you know ￿￿ Guess ￿ y2 (t) = v (t)e −2t . ⇒ ⇒ ￿ y2 (t) = v ￿ (t)e−2t − 2v (t)e−2t ￿ 4y2 (t) = 4v (t)e−2t 4y2 (t) = 4v ￿ (t)e−2t − 8v (t)e−2t ￿￿ y2 (t) = v ￿￿ (t)e−2t − 2v ￿ (t)e−2t − 2v ￿ (t)e−2t + 4v (t)e−2t ⇒ ￿￿ y2 (t) = v ￿￿ (t)e−2t − 4v ￿ (t)e−2t + 4v (t)e−2t ￿￿ ￿ y 2 + 4y2 + 4y2 = Reduction of order y1 (t) = e−2t . For the equation y + 4y + 4y = 0 , say you know ￿￿ Guess ￿ y2 (t) = v (t)e −2t . ⇒ ⇒ ￿ y2 (t) = v ￿ (t)e−2t − 2v (t)e−2t ￿ 4y2 (t) = 4v (t)e−2t 4y2 (t) = 4v ￿ (t)e−2t − 8v (t)e−2t ￿￿ y2 (t) = v ￿￿ (t)e−2t − 2v ￿ (t)e−2t − 2v ￿ (t)e−2t + 4v (t)e−2t ⇒ ￿￿ y2 (t) = v ￿￿ (t)e−2t − 4v ￿ (t)e−2t + 4v (t)e−2t ￿￿ ￿ y 2 + 4y2 + 4y2 = Reduction of order y1 (t) = e−2t . For the equation y + 4y + 4y = 0 , say you know ￿￿ Guess ￿ y2 (t) = v (t)e −2t . ⇒ ⇒ ￿ y2 (t) = v ￿ (t)e−2t − 2v (t)e−2t ￿ 4y2 (t) = 4v (t)e−2t 4y2 (t) = 4v ￿ (t)e−2t − 8v (t)e−2t ￿￿ y2 (t) = v ￿￿ (t)e−2t − 2v ￿ (t)e−2t − 2v ￿ (t)e−2t + 4v (t)e−2t ⇒ ￿￿ y2 (t) = v ￿￿ (t)e−2t − 4v ￿ (t)e−2t + 4v (t)e−2t ￿￿ ￿ y 2 + 4y2 + 4y2 = Reduction of order y1 (t) = e−2t . For the equation y + 4y + 4y = 0 , say you know ￿￿ Guess ￿ y2 (t) = v (t)e −2t . ⇒ ⇒ ￿ y2 (t) = v ￿ (t)e−2t − 2v (t)e−2t ￿ 4y2 (t) = 4v (t)e−2t 4y2 (t) = 4v ￿ (t)e−2t − 8v (t)e−2t ￿￿ y2 (t) = v ￿￿ (t)e−2t − 2v ￿ (t)e−2t − 2v ￿ (t)e−2t + 4v (t)e−2t ⇒ ￿￿ y2 (t) = v ￿￿ (t)e−2t − 4v ￿ (t)e−2t + 4v (t)e−2t ￿￿ ￿ y 2 + 4y2 + 4y2 = Reduction of order y1 (t) = e−2t . For the equation y + 4y + 4y = 0 , say you know ￿￿ Guess ￿ y2 (t) = v (t)e −2t . ⇒ ⇒ ￿ y2 (t) = v ￿ (t)e−2t − 2v (t)e−2t ￿ 4y2 (t) = 4v (t)e−2t 4y2 (t) = 4v ￿ (t)e−2t − 8v (t)e−2t ￿￿ y2 (t) = v ￿￿ (t)e−2t − 2v ￿ (t)e−2t − 2v ￿ (t)e−2t + 4v (t)e−2t ⇒ ￿￿ y2 (t) = v ￿￿ (t)e−2t − 4v ￿ (t)e−2t + 4v (t)e−2t ￿￿ ￿ y2 + 4y2 + 4y2 = v ￿￿ e−2t Reduction of order y1 (t) = e−2t . For the equation y + 4y + 4y = 0 , say you know ￿￿ Guess ￿ y2 (t) = v (t)e −2t . ⇒ ⇒ ￿ y2 (t) = v ￿ (t)e−2t − 2v (t)e−2t ￿ 4y2 (t) = 4v (t)e−2t 4y2 (t) = 4v ￿ (t)e−2t − 8v (t)e−2t ￿￿ y2 (t) = v ￿￿ (t)e−2t − 2v ￿ (t)e−2t − 2v ￿ (t)e−2t + 4v (t)e−2t ⇒ ￿￿ y2 (t) = v ￿￿ (t)e−2t − 4v ￿ (t)e−2t + 4v (t)e−2t ￿￿ ￿ y2 + 4y2 + 4y2 = v ￿￿ e−2t 0= Reduction of order y1 (t) = e−2t . For the equation y + 4y + 4y...
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## This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at The University of British Columbia.

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