|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+x^{2} y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.500 |
|
|
\[
{}2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.786 |
|
|
\[
{}4 x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.812 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.839 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.607 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.809 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.148 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.752 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.931 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.997 |
|
|
\[
{}2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.881 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.807 |
|
|
\[
{}z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.576 |
|
|
\[
{}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.938 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.825 |
|
|
\[
{}x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.054 |
|
|
\[
{}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.055 |
|
|
\[
{}2 \left (2-x \right ) x^{2} y^{\prime \prime }-\left (4-x \right ) x y^{\prime }+\left (3-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.011 |
|
|
\[
{}\left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.401 |
|
|
\[
{}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.648 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 \left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.979 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.732 |
|
|
\[
{}\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.643 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.503 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.543 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.597 |
|
|
\[
{}y^{\prime \prime } = \left (x -1\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.494 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.773 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.094 |
|
|
\[
{}y^{\prime \prime }+\left ({\mathrm e}^{x}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.698 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.182 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.699 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.023 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.439 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.869 |
|
|
\[
{}x y^{\prime \prime }+\left (\frac {1}{2}-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.809 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.717 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.776 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {25}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.664 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.484 |
|
|
\[
{}y^{\prime }+x y = \cos \left (x \right )
\] |
[_linear] |
✓ |
0.709 |
|
|
\[
{}y^{\prime }+x y = \frac {1}{x^{3}}
\] |
[_linear] |
✓ |
1.211 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.096 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.256 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \cos \left (x \right )
\] |
[_linear] |
✗ |
0.402 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.413 |
|
|
\[
{}y^{\prime \prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.590 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.500 |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.579 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.666 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.448 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.582 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.609 |
|
|
\[
{}y^{\prime \prime }+2 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }-x y = \frac {1}{1-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.545 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.747 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y \left (x +1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.792 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.696 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.584 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.694 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.722 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.195 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.168 |
|
|
\[
{}x y^{\prime \prime }+x^{3} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.173 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x -y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.318 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.470 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.383 |
|
|
\[
{}x^{3} y^{\prime \prime }+y \left (x +1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.109 |
|
|
\[
{}x y^{\prime \prime }+x^{5} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.145 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.393 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.896 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.700 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.213 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.629 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }-4 y^{\prime } x +5 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.007 |
|
|
\[
{}x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y = 0
\] |
[NONE] |
✗ |
0.062 |
|
|
\[
{}t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.057 |
|
|
\[
{}u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\] |
[NONE] |
✗ |
0.303 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.341 |
|
|
\[
{}R^{\prime \prime } = -\frac {k}{R^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
70.648 |
|
|
\[
{}x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.768 |
|
|
\[
{}\sin \left (y^{\prime }\right ) = x +y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.214 |
|
|
\[
{}\sin \left (x^{\prime }\right )+y^{3} x = \sin \left (y \right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
23.548 |
|
|
\[
{}y^{2}-1+y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.844 |
|
|
\[
{}2 y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.381 |
|
|
\[
{}y^{\prime }+20 y = 24
\] |
[_quadrature] |
✓ |
1.349 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.077 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.227 |
|
|
\[
{}\left (y-x \right ) y^{\prime } = y-x
\] |
[_quadrature] |
✓ |
0.957 |
|
|
\[
{}y^{\prime } = 25+y^{2}
\] |
[_quadrature] |
✓ |
1.227 |
|
|
\[
{}y^{\prime } = 2 x y^{2}
\] |
[_separable] |
✓ |
1.964 |
|
|
\[
{}2 y^{\prime } = y^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
2.681 |
|
|
\[
{}x^{\prime } = \left (x-1\right ) \left (1-2 x\right )
\] |
[_quadrature] |
✓ |
1.388 |
|
|
\[
{}2 x y+\left (x^{2}-y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.025 |
|
|
\[
{}p^{\prime } = p \left (1-p\right )
\] |
[_quadrature] |
✓ |
1.645 |
|
|
\[
{}y^{\prime }+4 x y = 8 x^{3}
\] |
[_linear] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.194 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y = 12 x^{2}
\] |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.264 |
|
|
\[
{}y^{\prime } x -3 x y = 1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.080 |
|