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Unformatted text preview: Mathematics 33B  Practice Midterm 2 Official exam to be administered Nov. 21st, 11:00am NAME (please print legibly): Your University ID Number: Your Discussion Section and TA: Signature: QUESTION VALUE SCORE 1 25 2 25 3 25 4 25 TOTAL 100 1 1. (25 points) (a) Find the general solution to y 00 + y 6 y = 0. (b) Find a particular solution to y 00 + y 6 y = 4 te t . 2 (c) Solve the initial value problem y 00 + y 6 y = 4 te t , y (0) = 1 / 4, y (0) = 3 / 4. 3 2. (25 points) (a) Find the general solution to y 00 + 2 y + 5 y = 0. 4 (b) Find the general solution to y 00 + 2 y + 5 y = 2 cos t . (c) As t → ∞ all solutions to y 00 + 2 y + 5 y = 2 cos t approach the steady state solution. Write the steady state solution in the form A cos( t δ ). You do not need to find δ explicitly, but do find tan δ and say which of the intervals ( π, π/ 2] , ( π/ 2 , 0] , (0 ,π/ 2], or ( π/ 2 ,π ] contains δ ....
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 Winter '07
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 Math, Derivative, Steady State, Elementary algebra, general solution

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