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Unformatted text preview: .2714 10% 2 .2 .5385 .4908 9.7% 3 .3 .7248 .6651 8.9 % 4 .4 .8665 .7997 8.3% 2 The exact numbers are from the solution to the diﬀerential equation. The equation can be put into the form of a ﬁrst order linear equation: y + 2 y = 3 cos t with p ( t ) = 2. Thus our integrating factor is μ = e R 2d t = e 2 t . Multiplying both sides of our diﬀerential equation and simplifying gives: y e 2 t + 2 ye 2 t = 3 e 2 t cos t d d t [ e 2 t y ] = 3 e 2 t cos t e 2 t y = Z 3 e 2 t cos t d t = 3 5 e 2 t (sin t + 2 cos t ) + C ⇒ y ( t ) = 3 5 (sin t + 2 cos t ) + C e 2 t Plugging in the initial condition y (0) = 0 gives C =6 5 . The ﬁnal answer is: y ( t ) = 3 5 (sin t + 2 cos t ) +6 5 e 2 t 3...
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 Spring '07
 TERRELL,R
 Math, Cos, Trigraph, 0 0 0 0%, 2714 10%, 4908 9.7%, 6651 8.9 %

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