|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.641 |
|
|
\[
{}y^{\prime \prime }-y = 2 \sinh \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.592 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.101 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.161 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.185 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.169 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.205 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.507 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.317 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.296 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.277 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.016 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.675 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.229 |
|
|
\[
{}y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.951 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.389 |
|
|
\[
{}y^{\prime \prime }+9 y = \tan \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.579 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.918 |
|
|
\[
{}y^{\prime \prime }+16 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.333 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.692 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \tan \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.280 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right ) \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.244 |
|
|
\[
{}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.294 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.627 |
|
|
\[
{}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.343 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.498 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.100 |
|
|
\[
{}y^{\prime \prime }+9 y = \csc \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.132 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.477 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.912 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.245 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.985 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.143 |
|
|
\[
{}y^{\prime \prime }+4 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.059 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.395 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.030 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.395 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = -t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.955 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.389 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.608 |
|
|
\[
{}t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.306 |
|
|
\[
{}\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.366 |
|
|
\[
{}y^{\prime \prime \prime } = 0
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.033 |
|
|
\[
{}y^{\prime \prime \prime }-10 y^{\prime \prime }+25 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}8 y^{\prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}3 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}6 y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}5 y^{\prime \prime \prime }-15 y^{\prime }+11 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\prime \prime \prime \prime }-9 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+6 y^{\prime \prime }-32 y^{\prime }-32 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }+8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.137 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.146 |
|
|
\[
{}24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.150 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.100 |
|
|
\[
{}2 y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+17 y^{\prime \prime \prime }+17 y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}y^{\left (5\right )}+8 y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.146 |
|
|
\[
{}y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.157 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime \prime }+16 y^{\prime }-26 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.142 |
|
|
\[
{}\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10} = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.517 |
|
|
\[
{}2 y y^{\prime \prime }+y^{2} = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.757 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{t}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.110 |
|
|
\[
{}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 9 \,{\mathrm e}^{3 t}
\] |
[[_high_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y = t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.908 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.177 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y = 108 t
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y = -111 \,{\mathrm e}^{t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y = 153 \,{\mathrm e}^{-t}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.136 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = \tan \left (2 t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.586 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = \sec \left (2 t \right ) \tan \left (2 t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.680 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \sec \left (2 t \right )^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.686 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \tan \left (2 t \right )^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.700 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime } = \sec \left (3 t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.553 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = -\sec \left (t \right ) \tan \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.615 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = \sec \left (2 t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.645 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = -\frac {1}{t^{2}}-\frac {2}{t}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.232 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {{\mathrm e}^{t}}{t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.233 |
|