A Classical Math Problem from a Classical Text (Differential Equation)
I have always had a problem deciding when I should use pencil and paper and when I should use Mathcad. After all Euler, Laplace and Fourier didn't have Mathcad. Recently I decided to look at some problems in the text "Operational Mathematics" by Ruel V. Churchill (2nd Edition McGraw-Hill 1958). Chapter 1 introduces the Laplace transform and shows how it can be used to solve certain differential equations. Attempting to solve one of the Examples in Mathcad quickly revealed the limitation of symbolic operator "parfrac" and the difficulty of solving differential equations with unusual initial conditions. I attach a Mathcad Prime 3.0 file describing my experience with "Example 4 p 21." This problem involves a third order differential equation with two values for Y(t), a value for Y'(0), but no value for Y''(0). To solve the problem and obtain a unique solution you must introduce a second variable Y''(0) = C. In the long run a combination of pencil and paper and Mathcad allowed me to reproduce Example 4. If you know an easier way I would like to hear about it. I have not yet attempted to work with Mathcad's ODE solvers.