|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.964 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.826 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.070 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.153 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.872 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.273 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.296 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.944 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
25.707 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.938 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.326 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.166 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 12 x -10
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.502 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.911 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.593 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.424 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.183 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.615 |
|
|
\[
{}y^{\prime \prime }-3 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.164 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.589 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.943 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.041 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.023 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.868 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.960 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.033 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.227 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.204 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.392 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.412 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.695 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.560 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.185 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.974 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.654 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = \left (x^{2}-1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.423 |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.420 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (1-x \right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.539 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.178 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.062 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.409 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.416 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.368 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.372 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.336 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.324 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.303 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.649 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.328 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.060 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.034 |
|
|
\[
{}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24
\] |
[[_high_order, _quadrature]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.148 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.108 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.116 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.120 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.170 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.576 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.752 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-5 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.553 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.634 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.617 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.889 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.852 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.928 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.717 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.836 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.210 |
|
|
\[
{}y^{\prime \prime }-y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.710 |
|
|
\[
{}y^{\prime \prime } = \tan \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
6.869 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.633 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.914 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.914 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.299 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.273 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
24.227 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = x \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.312 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {2}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.619 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.862 |
|
|
\[
{}y^{\prime \prime }-y = 3 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.510 |
|
|
\[
{}y^{\prime \prime }+y = -8 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.693 |
|