prac_ex2

prac_ex2 - 1 Find a particular solution of y 3y 4y = 2et A...

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1. Find a particular solution of y 00 - 3 y 0 - 4 y = 2 e - t . A. Y ( t ) = 2 e - t B. Y ( t ) = 2 t C. Y ( t ) = te - t D. Y ( t ) = 2 5 e - t E. Y ( t ) = - 2 5 te - t 2. The form of a particular solution to the equation y 00 + 2 y 0 + 2 y = te t cos t is: A. ( At + B ) e t cos t B. t ( At + B ) e t cos t C. Ate t cos t + Bte t sin t D. ( At + B ) e t cos t + ( Ct + D ) e t sin t E. t ( At + B ) e t cos t + t ( Ct + D ) e t sin t 3. The homogeneous diﬀerential equation y 00 - 4 t y 0 + 6 t 2 y = 0 ( t > 0) has two solutions given by y 1 ( t ) = t 2 and y 2 ( t ) = t 3 . Using the method of Variation of Parameters, ﬁnd the general solution of the nonhomogeneous equation y 00 - 4 t y 0 + 6 t 2 y = t . A. y = C 1 t 2 + C 2 t 3 + ln t B. y = C 1 t 2 + C 2 t 3 + t ln t C. y = C 1 t 2 + C 2 t 3 + t 2 ln t D. y = C 1 t 2 + C 2 t 3 + t 3 ln t E. y = C 1 t 2 + C 2 t 3 + t 4 ln t 1

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4. A mass weighing 2 lb stretches a spring 6 in. If the mass is pulled down an additional 3 in. and then released, and if there is no damping, determine the position
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prac_ex2 - 1 Find a particular solution of y 3y 4y = 2et A...

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