TY - GEN A1 - Wolf, Thomas T1 - The Parametric Solution of Underdetermined linear ODEs N2 - The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Gr\"{o}bner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible at http://lie.math.brocku.ca/crack/uode. T3 - ZIB-Report - 08-15 KW - linear ODEs KW - underdetermined systems KW - Euclid's algorithm KW - computer algebra KW - Reduce KW - Crack Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10693 SN - 1438-0064 ER -