1) Find the general solution, including an interval, to the following di↵erential equations.
y000 + 3y00 + 3y0 +1=0
y00 + 2y0 + y = exlnx
2) Find a solution to the following nonlinear di↵erential equation. Don’t worry about an
y00 = y0
3) Show using the definition of the Laplace Transform that the Laplace Transform of 1 is 1
4) Use the Laplace Transform to solve the following di↵erential equation:
y00 + 4y = et
In the test (and the final exam), you will be provided with the table on the very last 2 pages
of the text, so use that in order to help you solve this question.