In a book I found a sophisticated way of computing following ODEs:
$$ \frac{dy}{dx} + p(x)y = g(x)\\ (*) $$
They are called: "linear differential equations of first order". First, $g(x)$ is taken to be zero:
$$ \frac{dy}{dx} + p(x)y = 0\\ (**) $$
This form is called: "linear uniform equation". If $g(x) \neq 0$, then the equation is then again called as "linear non-uniform".
Then it is said: general integral of linear non-uniform equation (*) is a sum of general integral of uniform equation (**) and any specific integral of non-uniform equation (*).
Then there is the first step: computation of general integral of uniform equation. For this, variables of (**) are separated and following is obtained:
$$ y = C e^{-\int p(x)dx} $$
Then there is the second step: any specific integral of non-uniform equation. Two methods: "making constant variable" and "anticipation method".
My question: I'm looking for more resources on this, as the book that I'm citing provides only two examples (one for each of the methods of the second step). Also, the topic requires much explanation what can be seen only from length of this question, for example. Is there a resource that would provide e.g. $5$ examples for each of the two methods of step two, plus a nice explanation of the topic?