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ID |
problem |
ODE |
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Kovacic 1985 paper. page 13. section 3.2, example 1 |
\(y^{\prime \prime } = \frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}}\) |
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Kovacic 1985 paper. page 14. section 3.2, example 2 |
\(y^{\prime \prime } = \left (\frac {6}{x^{2}}-1\right ) y\) |
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Kovacic 1985 paper. page 15. Weber equation |
\(y^{\prime \prime } = \left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y\) |
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Kovacic 1985 paper. page 19. section 4.2. Example 1 |
\(y^{\prime \prime } = \left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y\) |
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Kovacic 1985 paper. page 23. section 5.2. Example 1 |
\(y^{\prime \prime } = \left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (x -1\right )^{2}}+\frac {3}{16 x \left (x -1\right )}\right ) y\) |
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Kovacic 1985 paper. page 25. section 5.2. Example 2 |
\(y^{\prime \prime } = -\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}}\) |
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Kovacic 2005 paper. Example 2 |
\(y^{\prime \prime } = -\frac {y}{4 x^{2}}\) |
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David Saunders 1981 paper. Example 1 |
\(y^{\prime \prime } = \left (x^{2}+3\right ) y\) |
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David Saunders 1981 paper. Example 3 |
\(x^{2} y^{\prime \prime } = 2 y\) |
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Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 1 |
\(y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0\) |
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Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 2 |
\(x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0\) |
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Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 3 |
\(\left (-2+x \right )^{2} y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-3 y = 0\) |
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