Can we remove the arbitrary function?

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flower321
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x(dA/dt) + (dx/dt)A + y(dA/dZ) + (dy/dZ) A = 0
can we remove the arbitrary function A from the equation?
i.e. x(d/dt) + (dx/dt) + y(d/dZ) + (dy/dZ) = 0
is it true?
 
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