Jeopardy comments/answers April 2008

Existence Uniqueness Each kind of differential equation we studied had a corresponding existence and uniqueness theorem. The goal of these problems is to recognize How many initial conditions you need (generally, the number of derivatives tells you how many) And, a “niceness condition” on the differential equation: mostly that the functions you see are continuous, but sometimes you also need a derivative to be continuous

Solution Methods There is often more than one method that would work. I’d use: Characteristic equation Variation of Parameters Laplace transforms Power series Integrating factor

Linear Algebra

Laplace Transform