|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.132 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = x \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.191 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = a \sin \left (n x +\alpha \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.072 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (n x +\alpha \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.172 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.137 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.134 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.306 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.224 |
|
|
\[
{}y^{\prime \prime }+9 y = 9
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.616 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.091 |
|
|
\[
{}5 y^{\prime \prime \prime }-7 y^{\prime \prime } = 3
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime } = -6
\] |
[[_high_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 2
\] |
[[_high_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.368 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime } = 8 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.214 |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.838 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.385 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.406 |
|
|
\[
{}7 y^{\prime \prime }-y^{\prime } = 14 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.110 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.199 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.310 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.652 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \left (x^{2}+x \right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.636 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.507 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.435 |
|
|
\[
{}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \sin \left (n x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.314 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.668 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.529 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.557 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 4 \,{\mathrm e}^{x} \left (\sin \left (x \right )+\cos \left (x \right )\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.818 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.602 |
|
|
\[
{}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.655 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.302 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.380 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.316 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}+x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.427 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = x^{2}+x
\] |
[[_high_order, _missing_y]] |
✓ |
0.119 |
|
|
\[
{}y^{\prime \prime }+y = x^{2} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.846 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.772 |
|
|
\[
{}y^{\prime \prime \prime }-y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.131 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.149 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.152 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.393 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.243 |
|
|
\[
{}y^{\prime \prime }-y = x +\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.912 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = \left (1+\sin \left (x \right )\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.850 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } = {\mathrm e}^{x}+1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (2 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.472 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.454 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.098 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.302 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.927 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.812 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.431 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.733 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.177 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.917 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.135 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.270 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime } = {\mathrm e}^{x}+3 \sin \left (2 x \right )+1
\] |
[[_high_order, _missing_y]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.031 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.268 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.588 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.511 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.504 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.844 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.496 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.101 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.121 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.457 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x +\sin \left (x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.663 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.457 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.596 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.892 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.681 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 2 x +{\mathrm e}^{x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.134 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.074 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 4 x +3 \sin \left (x \right )+\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.166 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.179 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = x \,{\mathrm e}^{x}-1
\] |
[[_high_order, _missing_y]] |
✓ |
0.149 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = x +2 \,{\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime }+y = -2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.308 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.741 |
|
|
\[
{}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.108 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.210 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.530 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.804 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.583 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.740 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.223 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.838 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.895 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.605 |
|