This is of practical interest since a single solution of

This is of practical interest since a single solution of an ODE can often be guessed.

(a) How could you reduce the order of a linear constant-coefficient ODE if a solution is known?

(b) Reduce x3y"' - 3x2y" + (6 - x2)xy' - (6 - x2)y = 0, using y= x (perhaps obtainable by inspection).