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# Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients

@article{Singer1991LiouvillianSO, title={Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients}, author={Michael F. Singer}, journal={J. Symb. Comput.}, year={1991}, volume={11}, pages={251-273} }

- Published 1991 in J. Symb. Comput.
DOI:10.1016/S0747-7171(08)80048-X

Let L(y) = b be a linear differential equation with coefficients in a differential field K. We discuss the problem of deciding if such an equation has a non-zero solution in K and give a decision procedure in case K is an elementary extension of the field of rational functions or is an algebraic extension of a transcendental liouvillian extension of the field of rational functions. We show how one can use this result to give a procedure to find a basis for the space of solutions, liouvillianâ€¦Â CONTINUE READING

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