ode internal name "higher_order_ODE_missing_x"
If the ode which is missing \(x\) then the substitution \(y^{\prime }=u,y^{\prime \prime }=u\frac {du}{dy},y^{\prime \prime \prime }=u^{2}\frac {d^{2}u}{dy^{2}}+u\left ( \frac {du}{dy}\right ) ^{2}\) and so on is used to reduced the order by one. This works for linear and nonlinear ode.