No, it's not anything like Euler's equation. It is a linear equation with constant coefficients. AllenCuz

**almost** had it. Normally if the right side of a d.e. has

, you would try a solution of the form

but if a is already a solution of the characteristic equation,

already satisfies the homogeneous equation so you try

.

However, if a is a

**double** root of the characteristic equation, both

and

are solutions to the homogeneous equation so try

Here, with a= 3, you should try a solution of the form

.

With

,

.

Put those into the d.e.