The differential equation must be properly identified as to its type so that the most appropriate method can be used

Here is a differential equation solution, use it as a reference

This is a first-order, first-degree, homogeneous type differential equation. The method adopted will be the substitution method, in order to allow the separation of variables.

This is the question command:

First step is to adopt a more manageable nomenclature algebraically

and,

in order to rewrite the differential equation in this form:

and, with successive steps

Aiming at the substitution process then we extend the mathematical differentiation process

and add to this successive necessary operations

until arriving in the form of separable variables

becoming trivial the step of mathematical integration

resulting:

Now we need to go back to restore the original variables, always transforming the constants to simplify the operations

necessary steps are added by algebraic manipulation

so the answer is: