MAT485-2007Spring

MAT485-2007Spring - [6, 6jT. (c) Find all solutions to the...

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1 MAT 485 Final Test A. Lutoborski Syracuse University Spring 2007 Total point value 100 pts, 8 problems. 1. (10 pts) Solve the initial value problem u'(t) = e-u(t), u(O) = 2 2. (10 pts) Find the general solution of the following differential equation: 3. (10 pts) Solve the initial value problem using the method of undetermined coefficients y" - 4y = e 2t , y(O) = 0, y'(O) = o. 4. (12 pts) (a) Find all solutions to the homogeneous equation Ax = 0 A = [2 3 1] 1 1 4 (b) Find a single solution to the nonhomogeneous equation Ax = b where b =
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Unformatted text preview: [6, 6jT. (c) Find all solutions to the nonhomogeneous equation Ax = b. 5. (14 pts) Solve the initial value problem for the following system y~ = -Yl + 3Y2, y; = 3Yl -Y2, Yl(O) = 1, Y2(0) = 3. 6. (14 pts) Solve the initial value problem 1 ] ---+ X'(O) = [-3,3jT-1 x, 2 7. (14 pts) Use the Laplace transform to solve the initial-value problem y"(t) + 4y(t) = 3cost y(O) = y'(O) = 0 8. (16 pts) Use the Laplace transform to solve the initial-value problem y"(t) + 9y(t) = f(t) y(O) = y'(O) = 0 where = g for 0 ~ t < 1 f(t) for t 2: 1...
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MAT485-2007Spring - [6, 6jT. (c) Find all solutions to the...

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