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I have a very odd question. I have a complicated expression that is proportional to dx and dy. I want to drop everything that is not dx^(n) *Exp[..], dy^(n)*Exp[..], dx^(n)*dy^(n)*Exp[..]. For the sake of the argument, here is an example:

dx/(x*y) + dx^3/(9*x*y)+ dy/(x*y)+dx*Exp[x]/(x*y) + dx^3*dy^3*Exp[3*(x+y)]/(x*y)

Is there anyway how to automatize it?

The result should look like this:

dx*Exp[x]/(x*y) + dx^3*dy^3*Exp[3*(x+y)]/(x*y)
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expr = dx/(x*y) + dx^3/(9*x*y) + dy/(x*y) + dx*Exp[x]/(x*y) + 
   dx^3*dy^3*Exp[3*(x + y)]/(x*y)

DeleteCases[Except[_. (dx | dy)^(_.) Exp[_]]] @ expr
 (dx E^x)/(x y) + (dx^3 dy^3 E^(3 (x + y)))/(x y)
TeXForm @ %

$$\frac{\text{dx}^3 \text{dy}^3 e^{3 (x+y)}}{x y}+\frac{\text{dx} e^x}{x y}$$

| improve this answer | |
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DeleteCases[func, Except[Alternatives[dx, dx^_, dy, dy^_] Exp[_] _]
(* returns: (dx E^x)/(x y) + (dx^3 dy^3 E^(3 (x + y)))/(x y) *)
| improve this answer | |
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