|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-54 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}3 y^{\prime \prime \prime }-2 y^{\prime \prime }+12 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+25 y^{\prime \prime }+20 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime } = y^{\prime \prime \prime }
\] |
[[_high_order, _missing_x]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime }+2 i y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.562 |
|
|
\[
{}y^{\prime \prime }-i y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.635 |
|
|
\[
{}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.802 |
|
|
\[
{}y^{\prime \prime \prime } = y
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime \prime } = y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.552 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.327 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
14.319 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.104 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.106 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.104 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.111 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime }+16 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.504 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+2 y = 3 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
21.881 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.707 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.306 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.653 |
|
|
\[
{}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
24.808 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.868 |
|
|
\[
{}y^{\prime \prime }-4 y = \cosh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.123 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.340 |
|
|
\[
{}2 y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.516 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = 3 x -1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.099 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 2-\sin \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
26.216 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = x \,{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.125 |
|
|
\[
{}y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }-y = 17
\] |
[[_high_order, _missing_x]] |
✓ |
0.133 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.629 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )+x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.892 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime }+4 y = {\mathrm e}^{x}-x \,{\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.217 |
|
|
\[
{}y^{\left (5\right )}+2 y^{\prime \prime \prime }+2 y^{\prime \prime } = 3 x^{2}-1
\] |
[[_high_order, _missing_y]] |
✓ |
0.183 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}+7
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.048 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = {\mathrm e}^{x}+2 x^{2}-5
\] |
[[_high_order, _missing_y]] |
✓ |
0.153 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.006 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-12 y^{\prime } = x -2 x \,{\mathrm e}^{-3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.351 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
31.161 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right )+\cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = \left (x^{2}+1\right ) \sin \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.694 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.188 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.226 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.377 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.632 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.363 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.680 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 1+x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.216 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.948 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.195 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 5
\] |
[[_high_order, _missing_x]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }-2 y = 8 x^{5}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.153 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = \cos \left (x \right )^{3}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.178 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.536 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (x \right )^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.048 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.854 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.090 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.187 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.147 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.237 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.020 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.665 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.584 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.401 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.592 |
|
|
\[
{}y^{\prime \prime }-4 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.190 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.684 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.721 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.382 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.640 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.050 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.600 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.826 |
|
|
\[
{}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.838 |
|
|
\[
{}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.225 |
|
|
\[
{}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.546 |
|
|
\[
{}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.621 |
|
|
\[
{}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
90.347 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.723 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.807 |
|
|
\[
{}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
34.868 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
35.035 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.142 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.732 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.154 |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.842 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 2 \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
41.273 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
55.259 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+45 x = 50 \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
60.112 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+650 x = 100 \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
61.979 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.316 |
|