{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# test3-1 - for the solution to the equation with Answer the...

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
, and therefore . Using partial fractions , so , or , and therefore , , , so and . Then ; final solution : ( alternate test version ). 3. (13 pts.) Find the Laplace transform