Homogeneous differential equations

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The equation 3y'''' + 21y'' + y' + 6y = 0 is indeed a homogeneous differential equation, as the absence of the y''' term means its coefficient is zero. The definition of a homogeneous differential equation focuses on the form of the equation rather than the number of terms present. Understanding whether an equation is homogeneous is crucial for solving it correctly. The discussion highlights the importance of recognizing coefficients in determining the classification of differential equations. Clarifying these terms aids in proper mathematical communication and problem-solving.
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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