I've found the same result as in yours. Is it weird or is that the true result? y= Ax+ B/x + C x ln|x|
Once you get the solution in the transformed space, use the table to get the inverse laplace transform of your solution.
For your test at least know how to setup the question.
Apply laplace denoted by L
L(ty'' + (1-2t)y' - 2y) = L(0)
L(ty'' + y' - 2ty' - 2y) = 0
L(ty'') + L(y') - 2L(ty') - 2L(y) = 0
If you have time, you look up the laplace transforms of these individual terms on a table (probably provided with the exam) that looks like this: http://en.wikipedia.org/wiki/Laplace...s_and_theorems