|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.745 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.967 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime } = \sqrt {x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.031 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.764 |
|
|
\[
{}y^{\prime \prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.842 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.911 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {5 y}{2} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.400 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.615 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.456 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.178 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.173 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.502 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.826 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.710 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.742 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.961 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.034 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.939 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }+3 = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.434 |
|
|
\[
{}y^{\prime \prime }+20 y^{\prime }+100 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.810 |
|
|
\[
{}x y^{\prime \prime } = 3 y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.882 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.187 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.818 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.288 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.891 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.949 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.540 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.965 |
|
|
\[
{}y^{\prime \prime }+36 y = 6 \sec \left (6 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.754 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 18 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.416 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.937 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x -2 y = 10 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.453 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.977 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = -3 x {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.701 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.889 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \frac {1}{x^{2}+1}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.990 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.970 |
|
|
\[
{}3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.592 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = {\mathrm e}^{-2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.117 |
|
|
\[
{}y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.154 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{\left (x +1\right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.701 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.585 |
|
|
\[
{}y^{\prime }+4 y = 0
\] |
[_quadrature] |
✓ |
0.217 |
|
|
\[
{}y^{\prime }-2 y = t^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime }+3 y = \operatorname {Heaviside}\left (t -4\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime \prime }-4 y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.308 |
|
|
\[
{}y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.345 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.369 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.442 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.308 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 7
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.451 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.486 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[_Lienard] |
✗ |
0.048 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.286 |
|
|
\[
{}y^{\prime \prime }+9 y = 27 t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.312 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} t^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.255 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+17 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.308 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.314 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.444 |
|
|
\[
{}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.311 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.462 |
|
|
\[
{}y^{\prime \prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.300 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.391 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.253 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.292 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.280 |
|
|
\[
{}y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\] |
[_quadrature] |
✓ |
0.253 |
|
|
\[
{}y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\] |
[_quadrature] |
✓ |
0.264 |
|
|
\[
{}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.249 |
|
|
\[
{}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.260 |
|
|
\[
{}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[_quadrature] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.337 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.543 |
|
|
\[
{}y^{\prime } = 3 \delta \left (t -2\right )
\] |
[_quadrature] |
✓ |
0.264 |
|
|
\[
{}y^{\prime } = \delta \left (t -2\right )-\delta \left (t -4\right )
\] |
[_quadrature] |
✓ |
0.318 |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -3\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.240 |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.286 |
|
|
\[
{}y^{\prime }+2 y = 4 \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.281 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.273 |
|
|
\[
{}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.277 |
|
|
\[
{}y^{\prime }+3 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.302 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.209 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.324 |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.273 |
|