# 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 x 3 y' - 3x 2 y + (6 - x 2 )xy' - (6 - x 2 )y = 0, using y 1 =

Chapter 3, P R O B L E M S E T 3 . 2 #14

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 x^{3}y"' - 3x^{2}y" + (6 - x^{2})xy' - (6 - x^{2})y = 0, using y_{1 }= x_{ }(perhaps obtainable by inspection).

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