|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.096 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.097 |
|
|
\[
{}y^{\prime \prime }-4 y = 3 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.668 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.944 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.361 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.243 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
68.212 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
30.224 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.349 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime }-4 y = x +{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.555 |
|
|
\[
{}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.188 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.814 |
|
|
\[
{}-2 y^{\prime \prime }+3 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.624 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.034 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = x^{2}+8
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x} \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.638 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y = x +{\mathrm e}^{2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = {\mathrm e}^{4 x} \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.162 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.561 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = \sin \left (k x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.182 |
|
|
\[
{}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = 5 \cos \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.513 |
|
|
\[
{}y^{\prime \prime }+9 y = \left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.166 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.710 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = \left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.202 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.349 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 5 \,{\mathrm e}^{2 x} \sin \left (3 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.196 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.938 |
|
|
\[
{}y^{\prime \prime }+4 y = 12 \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.205 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.741 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.456 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.506 |
|
|
\[
{}y^{\prime \prime }+y = 3 x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.264 |
|
|
\[
{}2 y^{\prime \prime }+5 y^{\prime }-3 y = \sin \left (x \right )-8 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.518 |
|
|
\[
{}8 y^{\prime \prime }-y = x \,{\mathrm e}^{-\frac {x}{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.327 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.131 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.402 |
|
|
\[
{}y^{\prime \prime }+4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.227 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.368 |
|
|
\[
{}y^{\prime \prime }+y = 4 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.021 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 x -2 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.086 |
|
|
\[
{}y^{\prime \prime }-y = 3 x +5 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.535 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{x}+\sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.191 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime } = \cos \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = {\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.307 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.185 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.173 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.913 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.780 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (x \right ) \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.108 |
|
|
\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.495 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.700 |
|
|
\[
{}y^{\prime \prime }+9 y = \csc \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.209 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (\frac {x}{3}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.398 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \tan \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.523 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{\frac {x}{2}} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.539 |
|
|
\[
{}y^{\prime }+P \left (x \right ) y = Q \left (x \right )
\] |
[_linear] |
✓ |
1.474 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.421 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.131 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.449 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.595 |
|
|
\[
{}y^{\prime \prime }+3 y = 3 \,{\mathrm e}^{-4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.753 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.491 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.349 |
|
|
\[
{}y^{\prime \prime }+2 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.652 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.483 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.501 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.784 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y = \sin \left (x \right )-{\mathrm e}^{4 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.790 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.661 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.189 |
|
|
\[
{}y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y = \sin \left (k x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.833 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.359 |
|
|
\[
{}y^{\prime \prime }+4 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.585 |
|
|
\[
{}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.221 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}-8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.367 |
|
|
\[
{}y^{\prime \prime \prime }-y = x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = x^{2} {\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.133 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.149 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.212 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = {\mathrm e}^{2 x} \left (x -3\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime } = \sin \left (3 x \right )+x \,{\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.411 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x^{2} {\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime } = x^{2}+\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.180 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.192 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = x^{3}-\frac {\cos \left (2 x \right )}{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.306 |
|