427K.07.Sample.III

# 427K.07.Sample.III - -t sin t y(0 = 0 y ’(0 = 3 2 Find...

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Name _____________________________ M 427K Exam III Signature ___________________________ 4/6/06 Show your work in an orderly form and label your answers clearly. For full credit you must show enough details to justify your answer. Put equality signs where they belong but not where they do not belong. Do not use notes or calculators. The five numbered problems all count the same. A table of Laplace transforms follows problem 5. You may use the table except where indicated. 1. Use Laplace transforms to solve the initial value problem y + 2y ’ + 5y = 3e

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Unformatted text preview: -t sin t , y(0) = 0, y ’ (0) = 3. 2. Find the radius and the interval of convergence of the following series. n 5 n n = " # x n 3. For the following differential equation, find the first three nonzero terms in each of two linearly independent powers series solution about the origin (x = 0). " " y + x " y + y = 4. (a) Compute [u " (t) # u " /2 (t)]sintdt #\$ \$ % . (b) Use Table 6.2.1 to find L-1 (e-2s Γ (4)/s 4 ). 5. Use the definition of the Laplace transform as an integral, not Table 6.2.1, to find the Laplace transform of f(t) = t. Show you work clearly....
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427K.07.Sample.III - -t sin t y(0 = 0 y ’(0 = 3 2 Find...

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