Homogeneous differential equations

[AlfredPyo]

Is this a homogeneous DE?
3y'''' + 21y'' + y' + 6y = 0

So... since a(n-1)y''' is missing, would this still by definition be a homogeneous differential equation?

 

[Simon Bridge]

It's not "missing", it's just the coefficient of y''' is zero.
Check the definition of "homogeneous DE" - does it refer to the number of terms present?
Lastly: why does it matter what it's called?