|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.112 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.001 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \left (x^{2}+x \right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
38.470 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.404 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.359 |
|
|
\[
{}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \sin \left (n x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.438 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.263 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.025 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.016 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 4 \,{\mathrm e}^{x} \left (\sin \left (x \right )+\cos \left (x \right )\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.286 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.632 |
|
|
\[
{}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.189 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.150 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.126 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.128 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}+x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.136 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.060 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = x^{2}+x
\] |
[[_high_order, _missing_y]] |
✓ |
0.119 |
|
|
\[
{}y^{\prime \prime }+y = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.810 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.497 |
|
|
\[
{}y^{\prime \prime \prime }-y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.091 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.185 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.716 |
|
|
\[
{}y^{\prime \prime }-y = x +\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.648 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = \left (\sin \left (x \right )+1\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.883 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } = 1+{\mathrm e}^{x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.485 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.398 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.569 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.102 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.465 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.447 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
19.026 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.248 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.554 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.931 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.861 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime } = {\mathrm e}^{x}+3 \sin \left (2 x \right )+1
\] |
[[_high_order, _missing_y]] |
✓ |
0.220 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.696 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.704 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.392 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.275 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.201 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.051 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.898 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.760 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.641 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.726 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x +\sin \left (x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.578 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.222 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.275 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.699 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.280 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 2 x +{\mathrm e}^{x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.759 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 4 x +3 \sin \left (x \right )+\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.322 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = x \,{\mathrm e}^{x}-1
\] |
[[_high_order, _missing_y]] |
✓ |
0.166 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = x +2 \,{\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime \prime }+y = 2-2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.211 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.475 |
|
|
\[
{}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.221 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.366 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.709 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.263 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.773 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.486 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.279 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.931 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{x} x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.589 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.475 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\sin \left (x \right )+\cos \left (x \right )\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.973 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.082 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = -2 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.187 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime \prime }-y = 2 x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.186 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.211 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.276 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.803 |
|
|
\[
{}y^{\prime \prime }-y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.329 |
|
|
\[
{}y^{\prime \prime }-y = -2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.397 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.314 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.209 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-5 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.997 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
2.822 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.334 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.387 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.283 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.335 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.887 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.881 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.176 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.180 |
|
|
\[
{}x^{2} y^{\prime \prime \prime } = 2 y^{\prime }
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.212 |
|