|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.060 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.060 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime }-4 y = 3 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.421 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.747 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.991 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
63.763 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
29.701 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.140 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime }-4 y = x +{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.250 |
|
|
\[
{}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.965 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.556 |
|
|
\[
{}-2 y^{\prime \prime }+3 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.328 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.796 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = x^{2}+8
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x} \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.829 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y = x +{\mathrm e}^{2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = {\mathrm e}^{4 x} \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.314 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.124 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = \sin \left (k x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.159 |
|
|
\[
{}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = 5 \cos \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime \prime }+9 y = \left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.877 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.875 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = \left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.254 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.945 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 5 \,{\mathrm e}^{2 x} \sin \left (3 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.617 |
|
|
\[
{}y^{\prime \prime }+4 y = 12 \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.805 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.420 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.066 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.313 |
|
|
\[
{}y^{\prime \prime }+y = 3 x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.773 |
|
|
\[
{}2 y^{\prime \prime }+5 y^{\prime }-3 y = \sin \left (x \right )-8 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.057 |
|
|
\[
{}8 y^{\prime \prime }-y = x \,{\mathrm e}^{-\frac {x}{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.013 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.881 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.109 |
|
|
\[
{}y^{\prime \prime }+4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.220 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.088 |
|
|
\[
{}y^{\prime \prime }+y = 4 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.725 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 x -2 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.734 |
|
|
\[
{}y^{\prime \prime }-y = 3 x +5 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.266 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{x}+\sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.598 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime } = \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.136 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = {\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.094 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.905 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.007 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.094 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.699 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.443 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.585 |
|
|
\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.362 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.710 |
|
|
\[
{}y^{\prime \prime }+9 y = \csc \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.120 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (\frac {x}{3}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.661 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \tan \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.519 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{\frac {x}{2}} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.369 |
|
|
\[
{}y^{\prime }+P \left (x \right ) y = Q \left (x \right )
\] |
[_linear] |
✓ |
1.037 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.124 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.184 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.293 |
|
|
\[
{}y^{\prime \prime }+3 y = 3 \,{\mathrm e}^{-4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.353 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.270 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.139 |
|
|
\[
{}y^{\prime \prime }+2 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.360 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.297 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.255 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.427 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = \sin \left (x \right )-{\mathrm e}^{4 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.802 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.701 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.895 |
|
|
\[
{}y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y = \sin \left (k x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.226 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.467 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.148 |
|
|
\[
{}y^{\prime \prime }+4 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.240 |
|
|
\[
{}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.817 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}-8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.165 |
|
|
\[
{}y^{\prime \prime \prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = x^{2} {\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = {\mathrm e}^{2 x} \left (x -3\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime } = \sin \left (3 x \right )+x \,{\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.535 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x^{2} {\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.124 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime } = x^{2}+\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{3}-\frac {\cos \left (2 x \right )}{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.369 |
|