Linear D Operator

Question

When I was at university, I did a course on Differential Equations where the 'Linear D-operator' was taught, i.e. that you introduce a a differential operator $D =\frac{d}{dx}$ so that for an example differential equation: \begin{equation} \frac{d^2y}{dx^2} - a^2 y(x) = f(x) \end{equation} Becomes: \begin{equation} (D - a)(D + a) y(x) = f(x) \end{equation} And from there techniques are taught to resolve. I was wondering if anyone knew any good resources to learn this? are their any (preferably free) textbooks/tutorial videos/etc on this topic?

Answer 1

You can find the following references:

$(1)\quad$ "Introductory Course in Differential Equations" by Daniel Alexander Murray

$(2\quad $ "Ordinary and Partial Differential Equations", and "Advanced Differential Equations" by M. D. Raisinghania

$(3)\quad $ "Differential Equations" by J. G. Chakravorty and P. R. Ghosh

$(4)\quad $ "An Introduction to Differential Equations" by Ram Krishna Ghosh and Kantish Chandra Maity

Also find

$(5)\quad $ "Differential Equations" by Shepley L. Ross

$(6)\quad $ "Differential Equations with Applications and Historical Notes " by George Simmons

$(7)\quad $ "Differential Equations: Theory, Technique, and Practice" by George F. Simmons and Steven G. Krantz

Answer 2

There is this very interesting article: Applications of Linear Algebra in Calculus, by Jack W. Rogers, Jr