When I face ordinary differential equations (ODE), I usually use integrating factors. So I try finding "well" integrating factors.
For example, we consider the following ODE. $$ u'+p(x)u=q(x) $$ Let $\mu$ or $M$ be some function, and multiply both sides: $$ \mu u'+\mu pu=q $$ Then we suppose this ODE can be expressed as $(\mu u)'=q$. So $$ \mu u'+\mu'u=q $$ Since 2nd equation and 3rd equation are the same, the following equation must be satisfied for $\mu$. $$ \mu'=\mu p $$ this ODE is easier than 1st equation.
I wonder why integrating factors are usually expressed as $\mu$ or $M$. It is easy to understand why most mathematical notations came into use, such as integral symbol($\int$), but I cannot make a good explanation of this notation.