Integrating factors by inspection. These are not yet implemented. Before going through the formal way to find \(\mu \) for non exact second order nonlinear ode, there is a table given by Murphy which we can utilize before searching for \(\mu \) as a lookup table. Writing the ode as \(y^{\prime \prime }+g\left ( x,y,y^{\prime }\right ) =0\) the table is

\(g\left ( x,y,y^{\prime }\right ) \) form	integrating factor
\(g\left ( y\right ) \) (i.e. function of \(y\) only)	\(y^{\prime }\)
\(g\left ( y^{\prime }\right ) \) (i.e. function of \(y^{\prime }\) only)	\(\frac {y^{\prime }}{g}\)
\(p\left ( x,y\right ) y^{\prime }+Q\left ( x,y\right ) \left ( y^{\prime }\right ) ^{2}\)	\(\frac {1}{y^{\prime }}\)
\(p\left ( x,y\right ) +Q\left ( x,y\right ) y^{\prime }\) such that \(\frac {\partial p}{\partial y}=\frac {\partial Q}{\partial x}\)	\(\frac {1}{y^{\prime }}\)

The above integrating factors are from Murphy book page 165.