|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.857 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
20.746 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.286 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.026 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 12 x -10
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.737 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.820 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.622 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.762 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = \sin \left (b x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.303 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.973 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.221 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.878 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.884 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.139 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.349 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.753 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.246 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.053 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.922 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.683 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.141 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.526 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.029 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.520 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.283 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.859 |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.041 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.284 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.580 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.706 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.052 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\prime \prime \prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.055 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.058 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_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]] |
✓ |
0.414 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24
\] |
[[_high_order, _quadrature]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.145 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.193 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.115 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.130 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.269 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.138 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.385 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.733 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.722 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.619 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.670 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = x^{3}-3 x^{2}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.876 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime }+y = 2 x^{3}-3 x^{2}+4 x +5
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.330 |
|
|
\[
{}4 y^{\prime \prime }+y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.822 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.127 |
|
|
\[
{}y^{\left (6\right )}-y = x^{10}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.350 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y = -x^{4}+3 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.307 |
|
|
\[
{}y^{\prime \prime }+y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.234 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } = 12 x -2
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 9 x^{2}-2 x +1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.851 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.963 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.941 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 16 x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.116 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = -x^{3}+1
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.119 |
|
|
\[
{}y^{\prime \prime \prime }-\frac {y^{\prime }}{4} = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime \prime } = \frac {1}{x^{3}}
\] |
[[_high_order, _quadrature]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime } = x +1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.010 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
0.441 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
0.233 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
0.320 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✗ |
0.050 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.142 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.250 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.487 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.089 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.493 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.331 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.409 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+n^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.437 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.361 |
|
|
\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.115 |
|
|
\[
{}x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.793 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.166 |
|
|
\[
{}\left (3 x +1\right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.905 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.644 |
|