DEspring06test2

DEspring06test2 - Differential Equations Mid Term...

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Unformatted text preview: Differential Equations Mid Term Examination - II (Spring- 2006) MTH 2201 Duration: 1 hour 2/28/2006 Max. Credit: 25points Answer all the questions. No credit will be given if only the answer is written without showing the relevant supporting work. Write legibly. The numbers at the end of each question indicate the maximum credit for the corresponding question. 1. Solve the Bernoulli DE y - y = et y 2 . 2. Find the solution of the IVP: y + y + y = 0, y(0) = 1, y (0) = 0. [5] [5] 3. Find a particular solution of the DE y + 9y = t2 e3t + 6, using the method of undertemined coefficients. [5] 4. Find a particular solution of the DE y + 4y + 4y = t-2 e-2t , for t > 0. [5] 5. Let 1 (t), 2 (t) be two solutions of the DE y - y = 0, satisfying the initial conditions 1 (0) = 1, 1 (0) = 1 and 2 (1) = 0, 2 (1) = 1. Determine if these solutions 1 (t) and 2 (t) are linearly dependent or linearly independent. [5] 1 ...
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