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Are there any effective methods to determinate the number of groups of linearly independent solutions in the general solutions of linear functional-differential equations of the form $\sum_{m=0}^{n}\sum_{p=0}^{q}f_{m,p}(x)y^{(m)}(x+c_{m,p})=0$ , where $c_{m,p}$ are real numbers not only restricted in integers?

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Where are the derivatives? –  Gerry Myerson Jun 1 '12 at 3:38
$Gerry Myerson, thanks to reminder. I have corrected my question. –  doraemonpaul Jun 1 '12 at 8:03

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