test3-1 - for the solution to the equation , with , , ....

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MATH 315 FALL 2006 TEST 3 SOLUTION KEY Note: the following solutions are for one version of the test; some final solutions for the alternate test version problems are also given. 1. (20 pts.) Use Power series to solve the differential equation with . 1. Find the recursion formula for the coefficients in the power series representation of the solution . Answer: , so , ( alternate test version , ), and , or for . 2. Determine the first six terms in the series for . Answer: using intial value , then , ; final solution : ( alternate test version ). 2. (22 pts.) Use Laplace transforms to solve with , . Answer: the transformed equation becomes or
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, and therefore . Using partial fractions , so , or , and therefore , , , so and . Then ; final solution : ( alternate test version ). 3. (13 pts.) Find the Laplace transform
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Unformatted text preview: for the solution to the equation , with , , . Answer: the transformed equation becomes , or ; final solution : ( alternate test version ). 4. (15 pts.) Consider the equation with , . Find the recursion formula for the coefficients in the power series representation of the solution . Answer: , so , or ( alternate test version ), for . 5. (8 pts.) Convert the 4 order differential equation , with , , , , to a 1 order system of equations. Answer: let , , , and ; final solution : ; . 6. (22 pts.) Find the solution for the system of differential equations Answer: eigenvalues determined from , or , so . Eigenvectors: : , so ; : , so , and . Constants and are determined from initial values using , or , so , ; final solution : ( alternate test version , with , )....
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This test prep was uploaded on 04/06/2008 for the course MATH 302 taught by Professor Goldberg during the Spring '08 term at Johns Hopkins.

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test3-1 - for the solution to the equation , with , , ....

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