|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.980 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.894 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.720 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.770 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.079 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.991 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (1-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.963 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.842 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (-2+x \right ) y^{\prime }+2 \left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.095 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.230 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2+3 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.085 |
|
|
\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
1.056 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.117 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.113 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.085 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.989 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.109 |
|
|
\[
{}x y^{\prime \prime }+\left (3 x +4\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.016 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.083 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.056 |
|
|
\[
{}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.023 |
|
|
\[
{}x \left (-2 x +1\right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.100 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.837 |
|
|
\[
{}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.320 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.218 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.388 |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.310 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.489 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.463 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.373 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.355 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.356 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.941 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.239 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.379 |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-5 y = 0
\] |
[_Laguerre] |
✓ |
1.376 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-15 x y^{\prime }+7 y \left (x +1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.437 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-2 x +1\right ) y^{\prime }-y \left (x +1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.444 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{3}+x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.983 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+\left (-2 x +1\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[_Jacobi] |
✓ |
1.283 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.815 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.132 |
|
|
\[
{}x y^{\prime \prime }+x y^{\prime }+\left (x^{4}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.312 |
|
|
\[
{}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.050 |
|
|
\[
{}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.937 |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y \left (x +1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.104 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.325 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-2 y = 0
\] |
[_Laguerre] |
✓ |
1.352 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.096 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +7\right ) y^{\prime }+2 \left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.092 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.030 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0
\] |
[_Gegenbauer] |
✓ |
0.713 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.092 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }-8 y = 0
\] |
[_erf] |
✓ |
0.606 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.018 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.248 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.099 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.885 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.060 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.816 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.964 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.610 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.129 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.064 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.776 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.893 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.920 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+4\right ) y = 0
\] |
[[_Bessel, _modified]] |
✓ |
1.265 |
|
|
\[
{}x \left (-2 x +1\right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.099 |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.018 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y \left (x +1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.980 |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
1.350 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.494 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
1.404 |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.148 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{4 y+x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.159 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.888 |
|
|
\[
{}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.277 |
|
|
\[
{}x y-1+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
0.226 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.352 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.308 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.398 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-2 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+4 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+2 y+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.473 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-7 y+10 \\ y^{\prime }=x-2 y-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.520 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x}
\] |
[_separable] |
✓ |
2.435 |
|
|
\[
{}y^{\prime } = x \left (\cos \left (y\right )+y\right )
\] |
[_separable] |
✓ |
1.586 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x}
\] |
[_separable] |
✓ |
3.129 |
|
|
\[
{}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right )
\] |
[_separable] |
✓ |
12.628 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
0.916 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.262 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.257 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.998 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}y^{\prime } = 1+\frac {\sec \left (x \right )}{x}
\] |
[_quadrature] |
✓ |
0.850 |
|
|
\[
{}y^{\prime } = x +\frac {\sec \left (x \right ) y}{x}
\] |
[_linear] |
✓ |
7.174 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
2.192 |
|