2065s10ex3

# 2065s10ex3 - Name: Exam 3 Instructions. Answer each of the...

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Name: Exam 3 Instructions. Answer each of the questions on your own paper. Put your name on each page of your paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. A table of Laplace transforms has been appended to the exam. The following trigonometric identities may also be of use: sin( ± + ) = sin ± cos + sin cos ± cos( ± + ) = cos ± cos ¡ sin ± sin 1. [10 Points] Find the solution of the following initial value problem: t 2 y 00 + 2 ty 0 ¡ 12 y = 0 ; y (1) = 0 ; y 0 (1) = 1 : 2. [15 Points] Use variation of parameters to ﬂnd a particular solution of the nonhomo- geneous diﬁerential equation y 00 + 4 y 0 + 4 y = t ¡ 5 e ¡ 2 t : You may assume that the solution of the homogeneous equation y 00 + 4 y 0 + 4 y = 0 is y h = c 1 e ¡ 2 t + c 2 te ¡ 2 t . 3. [15 Points] Find the Laplace transform of the following function: f ( t ) = ( cos t if 0 t < …; ¡ 2 if t …: 4. [20 Points]

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2065s10ex3 - Name: Exam 3 Instructions. Answer each of the...

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