The dperiodic_sols function seeks closed form solutions of linear ODEs having doubly-periodic coefficients. It returns either one or more doubly-periodic solutions to the linear ODE or provides a proof that no such solution exists.

In the case of an order two linear ODE, the dperiodic_sols function also seeks a general solution in terms of solutions that are doubly-periodic or doubly-periodic of the second kind.

The dperiodic_sols function returns, if possible, a list of one or more independent solutions. To find only doubly periodic solutions, set the environment variable _EnvDperiodicOnly to true.

The dperiodic_sols function recognizes doubly-periodic functions that are rational in the Weierstrass P and P' functions, or rational in the Jacobi , , and  functions.

The dperiodic_sols(lode, v) and dperiodic_sols(coeff_list, x) calling sequences are equivalent.

The dperiodic_sols(coeff_list, x) calling sequence is convenient for programming.

Burger, R.; Labahn, G.; and van Hoeij, M. "Closed form solutions of linear odes having elliptic functions as coefficients." Proceedings of ISSAC'04, Santander, Spain, ACM Press, (2004): 58-64.