Ordinary Differential Equations (ODE)
Suppose a differential equation can be written in the form
which we can write more simply by letting :
As long as h(y) ≠ 0, we can rearrange terms to obtain:
so that the two variables x and y have been separated. dx (and dy) can be viewed, at a simple level, as just a convenient notation, which provides a handy mnemonic aid for assisting with manipulations. A formal definition of dx as a differential (infinitesimal) is somewhat advanced.
Read more about this topic: Separation Of Variables
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