Missing independent variable \(x\)

ode internal name "second_order_ode_missing_x"

Given \begin {equation} y^{\prime \prime }+f\left ( y^{\prime }\right ) +g\left ( y\right ) =0 \tag {1} \end {equation} Let \(p=y^{\prime }\) then \(y^{\prime \prime }=\frac {dp}{dx}=\frac {dp}{dy}\frac {dy}{dx}=\frac {dp}{dy}p\) and the ode becomes\begin {equation} p\frac {dp}{dy}+f\left ( p\right ) +g\left ( y\right ) =0 \tag {2} \end {equation} Which is now a first order ode.