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exmpl2 - MAP2302 Test 2a 1 A given second order linear...

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MAP2302 Test 2a 1. A given second order, linear, non-homogeneous equation with constant coefficients has two linearly independent solutions y 1 ( t ) = cos t and y 2 ( t ) = sin t to the accompanying homogeneous equation; if A = 1 and the non homogeneous term is given by f ( t ) = sec t , the method of variation of parameters gives a particular solution as: A. y p ( t ) = t sin t +(cos t ) ln(cos t ) B. y p ( t ) = cos t sin t + t cos t C. y p ( t ) = t 2 sin t +(cos t ) ln(sin t ) D. y p ( t ) = t cos t + (sin t ) ln(cos t ) E. y p ( t ) = t cos 2 t + (sin t ) ln(sin t ) 2. Which of the following equations can be solved using the Method of Undetermined Coeffi- cients and the Superposition Principle: I. y 00 ( t ) + 13 y 0 ( t ) + y ( t ) = sin t + t 2 cos 2 t + 5 t II. 2 y 00 ( t ) - 11 y 0 ( t ) + 3 y ( t ) = tan t + t 2 e 3 t + 5 III. y 00 ( t ) - 9 y 0 ( t ) + 3 y ( t ) = t 5 e t cos t + t 2 /e 4 t A. only I B. only II C. only III D. I and III E. none of the above 3. Given the equation y 00 ( t ) - 2 y 0 ( t ) + 2 y ( t ) = 3 te t sin t + 5 e t cos t , a particular solution is of the form: A. y p ( t ) = ( At + B ) e t sin t + Ce t cos t B. y p ( t ) = t ( At + B ) e t sin t + t ( Ct + D ) e t cos t C. y p ( t ) = t ( At + B ) e t sin t + Cte t cos t D. y p ( t ) = ( At + B ) e t sin t + ( Ct + D ) e t cos t E. y p ( t ) = tAe t sin t + tCe t cos t 1
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4. The Laplace Transform of the function
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