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}
}
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, liouvillian… CONTINUE READING
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Liouvillian solutions of linear differential equations with liouvillian coefficients

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