|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.783 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.628 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.176 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.986 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.990 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.520 |
|
|
\[
{}x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.981 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+29 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.183 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
21.773 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
56.063 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.221 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.391 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+37 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
32.414 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.655 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-25 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.012 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.411 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.025 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.628 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.585 |
|
|
\[
{}x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.814 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.947 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.131 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
9.205 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.132 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.127 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.122 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.127 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 x y^{\prime }+16 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.152 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.144 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.141 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.143 |
|
|
\[
{}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.414 |
|
|
\[
{}y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.496 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.089 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }-9 y = 36
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.101 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -6 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.749 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.057 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 169 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.377 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 10 x +12
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.542 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.239 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.316 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.465 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.417 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.532 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.465 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 22 x +24
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.599 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.410 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.454 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.382 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 4 x^{2}+2 x +3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.489 |
|
|
\[
{}y^{\prime \prime }+9 y = 52 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.629 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.267 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.155 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.744 |
|
|
\[
{}y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.719 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.852 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.068 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.825 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -200
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.092 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-5 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.650 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.369 |
|
|
\[
{}y^{\prime \prime }+9 y = 9 x^{4}-9
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.640 |
|
|
\[
{}y^{\prime \prime }+9 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.581 |
|
|
\[
{}y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.978 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.669 |
|
|
\[
{}y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.105 |
|
|
\[
{}y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.855 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.095 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime \prime }+9 y = 39 x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.055 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.167 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 20
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.160 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.265 |
|
|
\[
{}y^{\prime \prime }+9 y = 3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.865 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.177 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.291 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.252 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.345 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.360 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
21.088 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
13.209 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.337 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.413 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 100
\] |
[[_2nd_order, _missing_x]] |
✓ |
12.258 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.346 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
18.240 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.326 |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.253 |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.655 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
31.231 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
19.839 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.403 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.264 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.155 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.116 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.229 |
|