It is likely that your ODE class utilizes an integrating factor $$ to solve first$-$order linear differential equations

$\frac{dy}{dx}+P(x)y=Q(x),=e^{{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}P(x)dx}$

While $$ was not derived by Leibniz $($remember that he technically only checked an answer$),$ it is interesting that his $p$ function is our modern ${!}^8$

$m+ny+dy$:$dx=0,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dp}{p}={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}ndx.$

Show that $$ from Equation $(5)$ is the same as $p$ from Equation $(6).$

We may not know exactly where Leibniz' trick came from, but we know where it ended up $...$ in your texts!