|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.228 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.768 |
|
|
\[
{}3 y^{\prime } y^{\prime \prime } = 2 y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.683 |
|
|
\[
{}2 y^{\prime \prime } = 3 y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.745 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.364 |
|
|
\[
{}y y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.257 |
|
|
\[
{}y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.979 |
|
|
\[
{}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.108 |
|
|
\[
{}y^{3} y^{\prime \prime } = -1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.727 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.449 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
25.657 |
|
|
\[
{}2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
5.275 |
|
|
\[
{}y^{\prime \prime \prime } = 3 y y^{\prime }
\] |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
0.052 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.879 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.815 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.752 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.009 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.946 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.381 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.368 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.140 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\left (5\right )} = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.038 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 3
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime } = \left (x -1\right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.641 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.381 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.433 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.020 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.982 |
|
|
\[
{}4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.563 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.512 |
|
|
\[
{}y^{\prime \prime }+25 y = \cos \left (5 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.945 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )-\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.415 |
|
|
\[
{}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.039 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.505 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.755 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.267 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = k \sin \left (k x +\alpha \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.506 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = k
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.792 |
|
|
\[
{}y^{\prime \prime \prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 2
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.093 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 3
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.104 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime } = 2
\] |
[[_high_order, _missing_x]] |
✓ |
0.110 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime } = 3
\] |
[[_high_order, _missing_x]] |
✓ |
0.101 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = 4
\] |
[[_high_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{4 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.162 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.157 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = x \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.193 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = a \sin \left (n x +\alpha \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.203 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (n x +\alpha \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.175 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.944 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.581 |
|
|
\[
{}y^{\prime \prime }+9 y = 9
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.158 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}5 y^{\prime \prime \prime }-7 y^{\prime \prime } = 3
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime } = -6
\] |
[[_high_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 2
\] |
[[_high_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.039 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime } = 8 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.534 |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.896 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.999 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.985 |
|
|
\[
{}7 y^{\prime \prime }-y^{\prime } = 14 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.492 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.605 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.319 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \left (x^{2}+x \right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.873 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.045 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.575 |
|
|
\[
{}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \sin \left (n x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.371 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.395 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.255 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.790 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 4 \,{\mathrm e}^{x} \left (\sin \left (x \right )+\cos \left (x \right )\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.227 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.429 |
|
|
\[
{}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.876 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.095 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.103 |
|