Homogeneous differential equations

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AlfredPyo
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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?
 
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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?
 

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