(Normal form) By making the change of variables y(x) = σ (x)v(x), from y to v, in y" +...

(Normal form) By making the change of variables y(x) = σ (x)v(x), from y to v, in y" + p(x)y' + q(x)y = 0, show that the first derivative term can be eliminated by choosing σsuch that 2σ' + pσ = 0. Show that the result is the normal form (i.e., canonical or simplest form)

where