|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-54 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}3 y^{\prime \prime \prime }-2 y^{\prime \prime }+12 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+25 y^{\prime \prime }+20 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.094 |
|
|
\[
{}9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.087 |
|
|
\[
{}y^{\prime \prime \prime \prime } = y^{\prime \prime \prime }
\] |
[[_high_order, _missing_x]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime }+2 i y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.817 |
|
|
\[
{}y^{\prime \prime }-i y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.829 |
|
|
\[
{}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.687 |
|
|
\[
{}y^{\prime \prime \prime } = y
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime \prime } = y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y
\] |
[[_high_order, _missing_x]] |
✓ |
0.093 |
|
|
\[
{}a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.638 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.533 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.546 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.126 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.125 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.125 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.131 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime }+16 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.418 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+2 y = 3 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
28.241 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.522 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.098 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.843 |
|
|
\[
{}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
23.562 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.938 |
|
|
\[
{}y^{\prime \prime }-4 y = \cosh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.161 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.311 |
|
|
\[
{}2 y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.910 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = 3 x -1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 2-\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.444 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.825 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = x \,{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.139 |
|
|
\[
{}y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }-y = 17
\] |
[[_high_order, _missing_x]] |
✓ |
0.143 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.566 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )+x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.691 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime }+4 y = {\mathrm e}^{x}-x \,{\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.243 |
|
|
\[
{}y^{\left (5\right )}+2 y^{\prime \prime \prime }+2 y^{\prime \prime } = 3 x^{2}-1
\] |
[[_high_order, _missing_y]] |
✓ |
0.185 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}+7
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.609 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = {\mathrm e}^{x}+2 x^{2}-5
\] |
[[_high_order, _missing_y]] |
✓ |
0.167 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.012 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-12 y^{\prime } = x -2 x \,{\mathrm e}^{-3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.163 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.316 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.094 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right )+\cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.213 |
|
|
\[
{}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = \left (x^{2}+1\right ) \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.620 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.195 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.399 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.352 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.723 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.889 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.280 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.199 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 1+x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.219 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.277 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.211 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 5
\] |
[[_high_order, _missing_x]] |
✓ |
0.119 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }-2 y = 8 x^{5}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.156 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = \cos \left (x \right )^{3}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.214 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.556 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (x \right )^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.922 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.740 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.097 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.240 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.102 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.325 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.035 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.060 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.442 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.283 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.690 |
|
|
\[
{}y^{\prime \prime }-4 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.229 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.888 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.073 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.783 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.960 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.609 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.668 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.066 |
|
|
\[
{}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.096 |
|
|
\[
{}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.521 |
|
|
\[
{}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.207 |
|
|
\[
{}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.558 |
|
|
\[
{}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.644 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.506 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.446 |
|
|
\[
{}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
20.106 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
34.404 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.125 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.270 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.487 |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.862 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 2 \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
24.925 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
24.811 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+45 x = 50 \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
69.050 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+650 x = 100 \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
71.915 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.280 |
|