To be linear, .

How is this equation (see below) linear?

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- Dec 26th 2010, 12:51 PMdwsmithLinear Operators
To be linear, .

How is this equation (see below) linear?

- Dec 27th 2010, 04:20 AMAckbeet
You have to distinguish between linear operators and linear equations. Typically, for the equation you've given, you'd throw the 3 over to the RHS and consider the operator to be everything else (that is, all the stuff with the dependent variable in it). So the operator is

This is linear. So a differential equation is considered linear if the associated operator is linear. The DE can still be linear even if it's non-homogeneous, as in your case. Does that make sense? - Dec 27th 2010, 01:22 PMdwsmith
I understand you can have linear non-homogeneous equation.

Whenever there is a term that isn't associated with the partial derivatives, it is simply disregard? - Dec 27th 2010, 05:52 PMAckbeet
I think you would ignore any term that doesn't have the dependent variable u in it.