|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.347 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.076 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.184 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.487 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.088 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.368 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.625 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.510 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.349 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.780 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.678 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.443 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.095 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.978 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.709 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.107 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.980 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.679 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.138 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.977 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }+x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.132 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.553 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.274 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.757 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.393 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
15.779 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.323 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.649 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.425 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 12 x -10
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.193 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.346 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.290 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.152 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = \sin \left (b x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.362 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.451 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.916 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.380 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.268 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.577 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.482 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.331 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.321 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.239 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.063 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.829 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.769 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.793 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.396 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.010 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.072 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.395 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = \left (x^{2}-1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.429 |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.482 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (1-x \right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.546 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.214 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.214 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.096 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.040 |
|
|
\[
{}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24
\] |
[[_high_order, _quadrature]] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.154 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.111 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.125 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.122 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.261 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.330 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.401 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.381 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.320 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.339 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = x^{3}-3 x^{2}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.761 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime }+y = 2 x^{3}-3 x^{2}+4 x +5
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.125 |
|
|
\[
{}4 y^{\prime \prime }+y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.709 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.120 |
|
|
\[
{}y^{\left (6\right )}-y = x^{10}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.174 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y = -x^{4}+3 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.725 |
|
|
\[
{}y^{\prime \prime }+y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.253 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } = 12 x -2
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.111 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 9 x^{2}-2 x +1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.344 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.501 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.508 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 16 x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.117 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = -x^{3}+1
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime \prime }-\frac {y^{\prime }}{4} = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.099 |
|