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# |
ODE |
CAS classification |
Solved? |
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\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = A x
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } \sin \left (x \right )-2 y^{\prime } \cos \left (x \right )+y \sin \left (x \right )-\ln \left (x \right ) = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
|
|
\[
{}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-f \left (x \right ) = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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\[
{}\left (-2+x \right ) x y^{\prime \prime \prime }-\left (-2+x \right ) x y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (2 x -1\right ) y^{\prime \prime \prime }+\left (x +4\right ) y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }-\ln \left (x \right ) = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }+6 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right ) = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime \prime } \sin \left (x \right )+\left (2 \cos \left (x \right )+1\right ) y^{\prime \prime }-y^{\prime } \sin \left (x \right )-\cos \left (x \right ) = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}\left (\sin \left (x \right )+x \right ) y^{\prime \prime \prime }+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }-3 y^{\prime } \sin \left (x \right )-y \cos \left (x \right )+\sin \left (x \right ) = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
|
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\[
{}y^{\prime \prime \prime \prime } x +5 y^{\prime \prime \prime }-24 = 0
\] |
[[_high_order, _missing_y]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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|
\[
{}x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}} = 0
\] |
[[_high_order, _fully, _exact, _linear]] |
✓ |
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\[
{}\left (2+x \right )^{2} y^{\prime \prime \prime }+\left (2+x \right ) y^{\prime \prime }+y^{\prime } = 1
\] |
[[_3rd_order, _missing_y]] |
✓ |
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|
\[
{}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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\[
{}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x y^{\prime \prime \prime } = 2
\] |
[[_3rd_order, _quadrature]] |
✓ |
|
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\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
|
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\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{{7}/{2}}}
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}x y^{\prime \prime \prime } = 2
\] |
[[_3rd_order, _quadrature]] |
✓ |
|
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\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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|
\[
{}x^{2} y^{\prime \prime \prime } = 2 y^{\prime }
\] |
[[_3rd_order, _missing_y]] |
✓ |
|
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\[
{}\left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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|
\[
{}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}\left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3}
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime \prime }+1 = 0
\] |
[[_high_order, _quadrature]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
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\[
{}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}}
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
|
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\[
{}x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }-2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime } = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
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\[
{}x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
|
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\[
{}x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime \prime } = \lambda y^{\prime \prime }
\] |
[[_high_order, _missing_y]] |
✓ |
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\[
{}x^{2} y^{\prime \prime \prime \prime }+1 = 0
\] |
[[_high_order, _quadrature]] |
✓ |
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\[
{}\left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 x y^{\prime }+6 y = 6
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
|
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\[
{}\left (x^{2}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
|
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\[
{}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}}
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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\[
{}y^{\prime \prime \prime }+\cos \left (x \right ) y^{\prime \prime }-2 y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
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