On Wikipedia:Homogeneous differential equation, it is said that a first order differential equation of the form ($a$, $b$, $c$, $e$, $f$, $g$ are all constants)
$${\displaystyle (ax+by+c)dx+(ex+fy+g)dy=0\,}$$
where $af \not= be$ can be transformed into a homogeneous type.
What if $af = be$? Is there a general method for solving this kind of equations?