Answer to Question #176526 in Differential Equations for Andy Maynard

Question

Write the given differential equation in the form L(y) = g(x),

 where L is a linear differential operator with constant coefficients. If possible, factor L. (Use D for the differential operator.)

3y'' − 8y' − 3y = 4

Answer 1

We know that $y'=Dy, y''=D^2 y,$ here $D$ is differential operator.

$$3D^2y-8Dy-3y=4$$

$$(3D^2-8D-3)y=4$$

$$(3D+1)(D-3)y=4$$