Question: Simple non-commutative Differential Operator

I'm using the differential operator D to differentiate variables and look at the structure of the equations, i.e. turn things like

D[1]u-vt+v^2=0 into

D[1,2](u)-D[2](v)*t+v*D[1](t)+2*v*D[2](v)=0

However, it is assumed that this is a commutative operator, i.e. D[1,2]=D[2,1]. Can I use an option to have it not commute, or should I look into using the DETools package?

Thanks,

Mike

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