We consider the problem of finding closed form solutions of linear differential
equations having coefficients which are elliptic functions. For second order
equations we show how to solve such an ode in terms of doubly periodic
functions of the second kind. The method depends on two procedures, the first
using a second symmetric power of an ode along with a decision procedure for
determining when such equations have elliptic function solutions while the
second uses computation of exponential solutions.
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