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Is it possible to solve the following differential equation:

$g: \Bbb{R} \to \Bbb{R}$, $$ g'(a)=a\cdot g(a-1),\ g(0)=\frac{1}{2}$$

I can't find any method for ordinary differential equations which works here.

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    Wikipedia has a decent article on [Delay differential equations](http://en.wikipedia.org/wiki/Delay_differential_equation), with an example very similar to yours under the heading "Solving DDEs".2012-03-10
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    Similar to (although also significantly different from) the Dickman rho-function, http://en.wikipedia.org/wiki/Dickman_function, beloved of Analytic Number Theorists.2012-05-31
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    Since http://books.google.com.hk/books?id=5n2sN8rBU28C is only trial-view version, some of the pages are blocked. Do the methods of determinating the number of linearly independent solutions in the general solutions of linear DDEs are in those blocked pages?2012-05-31

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