Question

\begin{array}l\color{#FF0000}{\text{What}}\text{ }\color{#FF7F00}{\text{is}}\text{ }\color{#FFE600}{\text{a}}\text{ }\color{#00FF00}{\text{partial}}\text{ }\color{#0000FF}{\text{differential}}\text{ }\color{#6600FF}{\text{equation?}}\end{array}

Answer 1

IIRC, an equation using multiple derivatives of a function. An example is
y'' + 3y' + 2y = 0. You can solve some of them by turning the derivatives into exponents and then solving polynomial equations. Then the solutions will be functions of e^x and stuff. (It's only been about 17 years since I did these, but I've still forgotten them.)