5.2.2 Missing \(y\) as in \(ay^{\prime \prime \prime }+by^{\prime \prime }+cy^{\prime }=f\left ( x\right ) \)

ode internal name "higher_order_ODE_missing_y"

This works for linear and non-linear ode. Since \(y\) is missing, we then assume \(y^{\prime }=u,y^{\prime \prime }=u^{\prime },y^{\prime \prime \prime }=u^{\prime \prime }\) and so on. The ode reduces to one order less. Now the lower order ode is solved.