Ordinary differential equations (ODEs) have solutions that depend on only one variable. Partial differential equations (PDEs) have solutions that depend on multiple variables.
Linear algebra is a language first, methodology second.Keith Thompson
By order, we mean the highest order derivative that appear in the differential equation.
A solution to the above ODE is a function
For some appropriate domain points. You can also call this a solution, too:
A differential equation is called autonomous if the independent variable does not appear on both sides.
If you want to find that
It would not be a linear algebra post without mention of one of the most used tools from that scientific field today: the matrix. No, not the one that Neo has to navigate. The one mathematicians use! It’s definition is super simple. It’s just a rectangular array of entries, arranged in rows and columns.
If you want an even more abstracted and more powerful version though, I suggest you read about tensors!