We can even use Sage to solve the initial value problem \begin{align*} \frac{dP}{dt} & = kP\\ P(0) & = 1000. \end{align*}
<sage> <input>k, t = var('k, t') P = function('P', t) de = diff(P, t) == k*P solution = desolve(de, P, ivar=t, ics=[0, 1000]) solution</input> <output>1000*e^(k*t)</output> </sage>
Thomas W. Judson, Associate Professor
Department of Mathematics and Statistics
Stephen F. Austin State University
P.O. Box 13040–3040 SFA Station
Nacogdoches, TX 75962
EMAIL: judsontw@sfasu.edu
Theron Hitchman, Associate Professor
Department of Mathematics 0506
University of Nothern Iowa
Cedar Falls, IA 50613–0506
EMAIL: theron.hitchman@uni.edu