|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.296 |
|
|
\[
{}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.168 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.377 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.332 |
|
|
\[
{}y^{\prime \prime }+16 y = \csc \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.614 |
|
|
\[
{}y^{\prime \prime }+16 y = \cot \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.815 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
83.003 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
49.761 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
60.856 |
|
|
\[
{}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.693 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
47.868 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
33.841 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
31.047 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.850 |
|
|
\[
{}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.560 |
|
|
\[
{}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.671 |
|
|
\[
{}y^{\prime \prime }-y = 2 \sinh \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.973 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.463 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.490 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.485 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.498 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.780 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.713 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.698 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.740 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.214 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.073 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.009 |
|
|
\[
{}y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.206 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.675 |
|
|
\[
{}y^{\prime \prime }+9 y = \tan \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.766 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.009 |
|
|
\[
{}y^{\prime \prime }+16 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.550 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.056 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \tan \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.581 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right ) \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.586 |
|
|
\[
{}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.373 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.792 |
|
|
\[
{}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.269 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.833 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.786 |
|
|
\[
{}y^{\prime \prime }+9 y = \csc \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.293 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.743 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = \ln \left (t \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.833 |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.214 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y = 2 \ln \left (t \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.026 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.485 |
|
|
\[
{}y^{\prime \prime }+4 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.023 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.401 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y = t^{3}+2 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.899 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.399 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = -t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.812 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.391 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.432 |
|
|
\[
{}t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-y^{\prime } t +y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.298 |
|
|
\[
{}\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.851 |
|
|
\[
{}y^{\prime \prime \prime } = 0
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.048 |
|
|
\[
{}y^{\prime \prime \prime }-10 y^{\prime \prime }+25 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}8 y^{\prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}3 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}6 y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}5 y^{\prime \prime \prime }-15 y^{\prime }+11 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }-9 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+6 y^{\prime \prime }-32 y^{\prime }-32 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }+8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.087 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\left (6\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.097 |
|
|
\[
{}y^{\left (6\right )}+12 y^{\prime \prime \prime \prime }+48 y^{\prime \prime }+64 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.101 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.151 |
|
|
\[
{}24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.157 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.149 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}2 y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+17 y^{\prime \prime \prime }+17 y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\left (5\right )}+8 y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.154 |
|
|
\[
{}y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.172 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime \prime }+16 y^{\prime }-26 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.091 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.136 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.151 |
|
|
\[
{}\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10} = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.660 |
|
|
\[
{}2 y y^{\prime \prime }+y^{2} = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.645 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{t}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.110 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.116 |
|