References

[AB04] Abell, M. L. and J. P. Braselton. Differential Equations with Mathematica. (3rd ed.) Elsevier Academic Press, 2004.
[A89] Abramov, S. A. "Rational Solutions of Linear Differential and Difference Equations with Polynomial Coefficients." USSR Comput. Maths. Math. Phys. 29 (1989): 7–12.
[A96] Abramov, S. A. "Symbolic Search Algorithms for Partial d'Alembertian Solutions of Linear Equations." Programming and Computer Software 22, no. 1 (1996): 26.
[AB01] Abramov, S. A. and M. Bronstein. "On Solutions of Linear Functional Systems." In Proc. ISSAC'01, 1–6, 2001.
[AK91] Abramov, S. A. and K. Yu. Kvansenko. "Fast Algorithms to Search for the Rational Solutions of Linear Differential Equations with Polynomial Coefficients." In Proc. ISSAC'91, 267–270, 1991.
[AP94] Abramov, S. A. and M. Petkovsek. "D'Alembertian Solutions of Linear Differential and Difference Equations." In Proc. ISSAC'94, 169–174, 1994.
[ABP95] Abramov, S. A., M. Bronstein, and M. Petkovsek. "On Polynomial Solutions of Linear Operator Equations." In Proc. ISSAC'95, 290–296, 1995.
[B93] Bocharov, A. "Symbolic Solvers for Nonlinear Differential Equations." The Mathematica Journal 3, no. 2 (1993): 63–69.
[BD97] Boyce, W. F. and R. C. DiPrima, Elementary Differential Equations. John Wiley and Sons, 1997.
[BM91] Boyer, C. B. and U. C. Merzbach, A History of Mathematics. (2nd ed.) John Wiley, 1991.
[B91] Bronstein, M. "The Risch Differential Equation on an Algebraic Curve." In Proc. ISSAC'91, 241–246, 1991.
[B92] Bronstein, M. "On Solutions of Linear Ordinary Differential Equations in Their Coefficient Field." J. Symbolic Computation 13 (1992): 413–439.
[B92a] Bronstein, M. "Integration and Differential Equations in Computer Algebra." Programming and Computer Software 18, no. 5 (1992): 201–217.
[B92b] Bronstein, M. "Linear Ordinary Differential Equations: Breaking through the Order 2 Barrier." In Proc. ISSAC'92, 42–48, 1992.
[C80] Campbell, S. L. Singular Systems of Differential Equations I. Pitman, 1980.
[C82] Campbell, S. L. Singular Systems of Differential Equations II. Pitman, 1982.
[CC04] Chan, L. and E. S. Cheb-Terrab. "Non-Liouvillian Solutions for Second Order Linear ODEs." In Proc. ISSAC'04, 80–86, 2004.
[CDM97] Cheb-Terrab, E. S., L. G. S. Duarte, and L. A. C. P. da Mota. "Computer Algebra Solving of First Order ODEs Using Symmetry Methods." Comp. Phys. Comm. 101 (1997): 254.
[CR99] Cheb-Terrab, E. S. and A. D. Roche. "Integrating Factors for Second Order ODEs." J. Symbolic Computation 27 (1999): 501.
[CR00] Cheb-Terrab, E. S. and A. D. Roche. "Abel ODEs: Equivalence and Integrable Classes." Comp. Phys. Comm. 130 (2000): 204.
[D58] Drazin, M. P. "Pseudo Inverses in Associative Rays and Semigroups." American Mathematical Monthly 65 (1958): 506–514.
[F59] Forsyth, A. R. Theory of Differential Equations. Dover, 1959.
[I99] Ibragimov, N. H. Elementary Lie Group Analysis and Ordinary Differential Equations. John Wiley & Sons, 1999.
[I44] Ince, E. L. Ordinary Differential Equations. Dover, 1944.
[K59] Kamke, E. Differentialgleichungen: Losungsmethoden und Losungen. Akademische Verlagsgesellschaft, 1959.
[K74] Kamke, E. Differentialgleichungen Losungsmethoden und Losungen, Bd. II: Partielle differentialgleichungen. Chelsea Publishing Co., 1974.
[K00] Kevorkian, J. Partial Differential Equations: Analytical Solution Techniques. Springer-Verlag, 2000.
[K72] Kline, M. Mathematical Thought from Ancient to Modern Times, Vol. 2. Oxford University Press, 1972.
[K86] Kovacic, J. J. "An Algorithm for Solving Second Order Linear Homogeneous Differential Equations." J. Symbolic Computation 2 (1986): 3–43.
[L01] Kovacic, J. J. "An Algorithm for Solving Second Order Linear Homogeneous Differential Equations." Lecture, City College of New York, 2001.
[KPS03] Kythe, P. K., P. Puri, and M. R. Schäferkotter. Partial Differential Equations and Boundary Value Problems with Mathematica. (2nd ed.) Chapman and Hall/CRC, 2003.
[L65] Lebedev, N. N. Special Functions and Their Applications. Prentice-Hall, 1965.
[M00] Meyer, C. D. Matrix Analysis and Applied Linear Algebra. SIAM, 2000.
[M60] Murphy, G. M. Ordinary Differential Equations and Their Solutions. Van Nostrand, 1960.
[M47] McLachlan, N. W. Theory and Application of Mathieu Functions. Oxford University Press, 1947.
[O95] Olver, P. J. Equivalence, Invariants and Symmetry. Cambridge University Press, 1995.
[PZ95] Polynanin, A. D. and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations. CRC Press, 1995.
[S81] Saunders, B. D. "An Implementation of Kovacic's Algorithm for Solving Second Order Linear Homogeneous Differential Equations." In Proc. SYMSAC'81 (P. Wang, ed.), 105, 1981.
[S85] Schlesinger, L. Handbuch der Theorie der Linearen Differentialgleichungen. Teubner, 1985.
[SS98] Shirvani, M. and J. W.-H. So. "Solutions of Linear Differential Algebraic Equations." SIAM Review 40, no. 2 (1998): 344–346.
[S57] Sneddon, I. Elements of Partial Differential Equations. McGraw-Hill, 1957.
[T05] Trott, M. The Mathematica GuideBook for Symbolics. Springer-Verlag, 2005.
[UW96] Ulmer, F. and J-A. Weil. "Note on Kovacic's Algorithm." J. Symbolic Computation 22 (1996): 179–200.
[WW27] Whittaker, E. T. and G. N. Watson. A Course of Modern Analysis. (4th ed.) Cambridge University Press, 1927.
[W02] Wolfram, S. A New Kind of Science. Wolfram Media, Inc., 2002.
[W04] Wolfram, S. The Mathematica Book, 5th ed. Wolfram Media, Inc., 2004.
[Z89] Zwillinger, D. Handbook of Differential Equations. Academic Press, 1989