MATH 315 FALL 2006 TEST 3 SOLUTION KEYNote: 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 , (alternatetest version , ), and , or for . 2.Determine the first sixterms in the series for . Answer:using intial value , then , ; final solution: (alternatetest version ). 2.(22 pts.) Use Laplace transforms to solve with , . Answer:the transformed equation becomes or
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