practice2(3) - Practice Exam 2: MAP 2302 1. Solve the...

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Practice Exam 2: MAP 2302 1. Solve the following IVP: y ′′ + 5 y + 4 y = 0 , y (0) = 1 , y (0) = 0 Answer: 4 3 e t 1 3 e 4 t 2. Given is an RC-circuit with R = 1 (Ohm) and C = 0 . 5 (Farad), driven by a generator that delivers E ( t ) = sin t (Volts). Suppose that the initial voltage over the capacitor is 1 Volt. Determine the voltage v C ( t ) over the capacitor. Answer: v C ( t ) = 22 5 e 2 t + 4 5 (sin( t ) cos( t ) 2 ) 3. What is the structure of the particular solution to: y ′′ + 2 y + 2 y = ( t 2 + 1) e t cos( t ) Answer: t ( A 2 t 2 + A 1 t + A 0 ) e t cos( t ) + t ( B 2 t 2 + B 1 t + B 0 ) e t sin( t ) y ′′ 4 y + 4 y = ( t + 3) e 2 t + sin( t ) + t e t Answer: t 2 ( A 1 t + A 0 ) e 2 t + B 1 cos( t ) + B 2 sin( t ) + ( C 1 t + C 0 ) e t 4. Find the general solution on the interval ( π/ 6 ,π/ 6) of y ′′ + 9 y = tan(3 t ) Answer: v 1 ( t ) y 1 ( t ) + v 2 ( t ) y 2 ( t ) , where y 1 ( t ) = cos(3 t ) , y
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This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.

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practice2(3) - Practice Exam 2: MAP 2302 1. Solve the...

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