The fourth order strongly noncanonical operators

It is shown that the strongly noncanonical fourth order operator array L\,y=(r₃(t)(r₂(t)(r₁(t)y'(t))')')' array can be written in essentially unique canonical form as array L\,y = q₄(t)(q₃(t)(q₂(t)(q₁(t)(q₀(t)y(t))')')')'. array The canonical representation essentially simplifies examination of the fourth order strongly noncanonical equations array (r₃(t)(r₂(t)(r₁(t)y'(t))')')'+p(t)y(τ(t))=0. array