I would like to delve a little bit deeper in the realm of differential equations.
When I start with this intent, I love to know where I can go. What different roads or what different scenarios may the topic offer.
Looking to the Wikipedia page on differential equations, it reports the common division:
"Differential equations can be divided into several types. Apart from describing the properties of the equation itself, these classes of differential equations can help inform the choice of approach to a solution. Commonly used distinctions include whether the equation is: Ordinary/Partial, Linear/Non-linear, and Homogeneous/Inhomogeneous."
But it also stimulated my curiosity about other possibilities:
"This list is far from exhaustive; there are many other properties and subclasses of differential equations which can be very useful in specific contexts."
I would like to know if it's possible to create an exhaustive diagram of most of the types of differential equations.
If someone could provide a detailed presentation proceeding from basic types to more advanced ones, it would be very helpful. ( A list, scheme...) Link to related sources are well appreciated too.


closed as primarily opinion-based by GEdgar, Leucippus, max_zorn, metamorphy, Cesareo Jan 12 at 8:05

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