|
# |
ODE |
CAS classification |
Solved? |
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\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 4 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -2\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 \left (x -1\right ) y^{\prime } = 3 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✗ |
|
|
\[
{}x^{3} y^{\prime } = 2 y
\] |
[_separable] |
✗ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = y^{\prime }+y
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}3 y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{-x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } \sin \left (x \right )+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{3}+x \right ) y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } \cos \left (x \right )+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y^{\prime } \sin \left (x \right )+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 y^{\prime } x +9 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x -2\right )^{3} y^{\prime \prime }+3 \left (x -2\right )^{2} y^{\prime }+x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x -2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x^{2}+9\right ) y^{\prime }+\left (x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}3 x y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (-2 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}6 x^{2} y^{\prime \prime }+7 y^{\prime } x -\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+9 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+8 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (5-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}5 x y^{\prime \prime }+\left (30+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x +4\right ) y^{\prime }+3 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-\left (6+2 x \right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 x^{2}-3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 4 y
\] |
[_quadrature] |
✓ |
|
|
\[
{}2 y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -2\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 \left (x +1\right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 \left (x -1\right ) y^{\prime } = 3 y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}2 y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✗ |
|
|
\[
{}x^{3} y^{\prime } = 2 y
\] |
[_separable] |
✗ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}3 y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{-x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } \sin \left (x \right )+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = x y
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+k^{2} x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+3\right ) y^{\prime \prime }-3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+4 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+4 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\alpha \left (\alpha +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (3 x^{2}+1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+\left (2-3 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (3 x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (4+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (2-x \right ) y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+2 \left (x -1\right )^{2} y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (2-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (4+6 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1+3 x \right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x +\frac {y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (8 x^{2}+1\right ) y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\left (x -3\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (x -1\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }-y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-2 x^{2}+1\right ) y^{\prime \prime }+\left (2-6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (1-4 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (2-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2+4 x \right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }-\left (1-2 x \right ) y^{\prime }-\left (3-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (5+2 x \right ) y^{\prime \prime }-y^{\prime }+\left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +4\right ) y^{\prime \prime }-\left (4+2 x \right ) y^{\prime }+\left (6+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (3 x +2\right ) y^{\prime \prime }-y^{\prime } x +2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x +3\right ) y^{\prime \prime }+3 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x +3\right ) y^{\prime \prime }-3 y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (10-2 x \right ) y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (7+x \right ) y^{\prime \prime }+\left (8+2 x \right ) y^{\prime }+\left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (6+4 x \right ) y^{\prime \prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (\beta \,x^{2}+\alpha x +1\right ) y^{\prime \prime }+\left (\delta x +\gamma \right ) y^{\prime }+\epsilon y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}+3 x +1\right ) y^{\prime \prime }+\left (6+8 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+4 x +4\right ) y^{\prime \prime }+\left (8+4 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +\left (2 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } x -\left (-x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 y^{\prime \prime }+2 y^{\prime } x +\left (-x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x^{2}+2 x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+\left (2 x^{2}-3 x +1\right ) y^{\prime }-\left (x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (3 x^{2}+12 x +13\right ) y^{\prime }+\left (5+2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (3 x^{2}+2 x +1\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+4 x +3\right ) y^{\prime \prime }-\left (-x^{2}+4 x +5\right ) y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+2 x +1\right ) y^{\prime \prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-2 x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+3 x +1\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}-11 x +16\right ) y^{\prime \prime }+\left (x^{2}-6 x +10\right ) y^{\prime }-\left (2-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (2+2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (5 x^{2}+3 x +3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+x \left (4 x^{2}+2 x +7\right ) y^{\prime }-\left (-7 x^{2}-4 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}8 x^{2} y^{\prime \prime }-2 x \left (-x^{2}-4 x +3\right ) y^{\prime }+\left (x^{2}+6 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x^{2}+x +3\right ) y^{\prime \prime }+\left (-x^{2}+x +4\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}10 x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (66 x^{2}+13 x +13\right ) y^{\prime }-\left (10 x^{2}+4 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (5+4 x \right ) y^{\prime }-\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 y^{\prime } x -\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (5+18 x \right ) y^{\prime }-\left (1-12 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +8\right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (6+x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}8 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+5 x \left (x^{2}+1\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+8\right ) y^{\prime \prime }+7 x \left (x^{2}+2\right ) y^{\prime }-\left (-9 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} \left (x +5\right ) y^{\prime \prime }+9 x \left (5+9 x \right ) y^{\prime }-\left (5-8 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (7 x^{2}+6 x +3\right ) y^{\prime }+\left (-3 x^{2}+6 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+2 x +1\right ) y^{\prime \prime }+x \left (4 x^{2}+3 x +1\right ) y^{\prime }-x \left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}+x +1\right ) y^{\prime }+x \left (2-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+x +4\right ) y^{\prime }+\left (3 x^{2}+5 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}25 x^{2} y^{\prime \prime }+x \left (15+x \right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (4 x +9\right ) y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (3-2 x \right ) y^{\prime }+\left (4+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 x \left (1-6 x \right ) y^{\prime }+\left (1-12 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3+5 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (4+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (4 x +9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1+4 x \right ) y^{\prime \prime }-x \left (1-4 x \right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (4 x^{2}+1\right ) y^{\prime \prime }+32 x^{3} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (-3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }+\left (12 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-9 x^{2}+5\right ) y^{\prime }+\left (-3 x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (-x^{2}+14\right ) y^{\prime }+2 \left (x^{2}+9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (7 x^{2}+3\right ) y^{\prime }+\left (8 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x^{2} y^{\prime }+\left (1-5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (4+3 x \right ) y^{\prime \prime }-x \left (4-3 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (9-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (14+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }-4 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -\left (-x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (x^{2}+8\right ) y^{\prime }+\left (3 x^{2}+5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }-x \left (x^{2}+3\right ) y^{\prime }-2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-t y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 t y^{\prime }+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}t^{3} y^{\prime \prime }+\sin \left (t^{3}\right ) y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}2 t y^{\prime \prime }+\left (1+t \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}t y^{\prime \prime }+\left (-t +1\right ) y^{\prime }+\lambda y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}2 \sin \left (t \right ) y^{\prime \prime }+\left (-t +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-t y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 t y^{\prime }+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = {\mathrm e}^{t}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}t^{3} y^{\prime \prime }+\sin \left (t^{2}\right ) y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}2 t y^{\prime \prime }+\left (1+t \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}t y^{\prime \prime }+\left (-t +1\right ) y^{\prime }+\lambda y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}t \left (-t +1\right ) y^{\prime \prime }+\left (\gamma -\left (1+\alpha +\beta \right ) t \right ) y^{\prime }-\alpha \beta y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}2 \sin \left (t \right ) y^{\prime \prime }+\left (-t +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t p \left (t \right ) y^{\prime }+q \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {1-y}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x y-x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x +\frac {y}{x}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime } = \sqrt {1+x y}
\] |
[‘y=_G(x,y’)‘] |
✓ |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \sin \left (y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \sin \left (x y\right )
\] |
[NONE] |
✓ |
|
|
\[
{}y^{\prime \prime } = \cos \left (x y\right )
\] |
[NONE] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +4\right ) y^{\prime \prime }+7 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \left (x +1\right ) y^{\prime \prime }-5 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (8-x \right ) x^{2} y^{\prime \prime }+6 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-2 x y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1-2 x \right ) y^{\prime \prime }+4 y^{\prime } x -4 y = x^{2}-x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +12\right ) y = x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}3 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = x^{4}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+10 y^{\prime } x +y = x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 6 \left (-x^{2}+1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+2 y = x^{2} \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y = x \left (x^{2}+x +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-y^{\prime } x +\left (1-x \right ) y = x^{2} \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}z^{2} y^{\prime \prime }-\frac {3 z y^{\prime }}{2}+\left (1+z \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}z y^{\prime \prime }-2 y^{\prime }+y z = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 z y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}z \left (1-z \right ) y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y}{z^{3}} = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}\left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +4 y = 0
\] |
[_erf] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }-3 y^{\prime } x -5 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x -1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+x y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -4 y = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{1-x}+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }+\left (x -2\right ) {\mathrm e}^{x} y^{\prime }+\frac {4 y}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 \,{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+3 y^{\prime } x +x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (1+6 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x \left (3 x^{2}+1\right ) y^{\prime }-2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (-x^{2}+x \right ) y^{\prime }+\left (x^{3}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (4 x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}\right ) y^{\prime }-\frac {7 y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \cos \left (x \right ) y^{\prime }-2 y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{3} y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 x \,{\mathrm e}^{x} y^{\prime }+9 \left (1+\tan \left (x \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-6 y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {3 y^{\prime } x}{2}-\frac {\left (x +1\right ) y}{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (2-x \right ) y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (1-\frac {3}{4 x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y}{x^{2}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {\left (-3 x^{2}+x \right ) y^{\prime }}{2 x^{3}+2 x^{2}}+\frac {y}{2 x^{3}+2 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }-\frac {y}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+\left (\frac {1}{4 x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )}{x \left (-x^{2}+2\right )} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {3 y^{\prime }}{x \left (1-x \right )}+\frac {2 y}{x \left (1-x \right )} = 0
\] |
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {\left (1-x \right ) y^{\prime }}{2 x}-\frac {y}{4 x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{2 x}+\frac {y}{4 x} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1+\frac {1}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {\left (1-5 x \right ) y^{\prime }}{-x^{2}+x}-\frac {4 y}{-x^{2}+x} = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{\left (x +1\right ) x}-\frac {y}{\left (x +1\right ) x} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (4 x -1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (\cos \left (x \right )+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \sin \left (x \right )+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-2 x^{2}+x \right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a^{3} x^{2} y = 2
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+a \,x^{2} y = x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (-n +1\right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (-n +1\right ) x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (a^{2}+x^{2}\right ) y^{\prime \prime }+y^{\prime } x -n^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +a^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+p x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }-\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-3 x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_elliptic, _class_I]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {a y}{x^{{3}/{2}}} = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[[_elliptic, _class_II]] |
✓ |
|
|
\[
{}4 x \left (1-x \right ) y^{\prime \prime }-4 y^{\prime }-y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = x^{{3}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = \sqrt {x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 3 x^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } x = x y+y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}\left (x^{2}-2\right ) y^{\prime \prime }+2 y^{\prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (1+t \right ) x^{\prime }-\left (t -2\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+\left (x^{2}-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }+\left (x +2\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}z^{\prime }-x^{2} z = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}w^{\prime \prime }-x^{2} w^{\prime }+w = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}\left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -3 y = 0
\] |
[_Hermite] |
✓ |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime \prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }-y^{\prime } x +2 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }+2 \left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{\prime }+\sin \left (t \right ) x = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }-x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}w^{\prime }+w x = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
|
|
\[
{}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +3 y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = \cos \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\sin \left (x \right ) y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime } = x^{2}-y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } x = 1-x +2 y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = 2 x^{2}+3 y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x^{2}-2 x +y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +p \left (p +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}z^{\prime \prime }+t z^{\prime }+\left (t^{2}-\frac {1}{9}\right ) z = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}2 \left (2-x \right ) x^{2} y^{\prime \prime }-\left (4-x \right ) x y^{\prime }+\left (3-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (4 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 \left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }+\left (4 x -6\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime \prime } = \left (x -1\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left ({\mathrm e}^{x}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (\frac {1}{2}-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {9}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {25}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }+x y = \cos \left (x \right )
\] |
[_linear] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \cos \left (x \right )
\] |
[_linear] |
✗ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x y = \frac {1}{1-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x y^{\prime \prime }+x^{3} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x -y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x y^{\prime \prime }+x^{5} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }-\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-25\right ) y^{\prime \prime }+2 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[_Hermite] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+\lambda y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\left (x -\frac {4}{x}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{4}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime } = y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = -2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } x -3 y = k
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }+4 y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x -2\right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}2 x \left (x -1\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+y^{\prime }+8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 t \left (1+t \right ) y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{49}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\frac {y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 x \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-6\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (36 x^{4}-16\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+36 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+k^{2} x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+k^{2} x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 \left (x +1\right )^{2} y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y}{4 x} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Hermite] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 x^{2} y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{3} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\alpha \left (\alpha +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x y^{\prime \prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x^{2}+x -2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+5 y^{\prime } x +3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \,{\mathrm e}^{x} y^{\prime }+3 \cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+3 \left (x^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (-x^{3}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (4 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = 2
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✗ |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x -y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x^{2} y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 p y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
|
|
\[
{}\left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (\cos \left (2 x \right )-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 x y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{3}-x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-4 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (x -1\right ) y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +p \left (p +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime } = -x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
[‘y=_G(x,y’)‘] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[_Hermite] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x -4 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+10 y^{\prime } x +20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-9\right ) y^{\prime \prime }+3 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x -4 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +3 y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +7 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 y^{\prime \prime }+9 y^{\prime } x -36 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+3 y^{\prime } x -8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 y^{\prime } x +7 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 y^{\prime } x +9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}8 x^{2} y^{\prime \prime }+10 y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x \left (4-x \right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (1+3 x \right ) y^{\prime }+\left (1-6 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -2\right ) x y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -2\right ) x y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (1-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (4+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-5 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }-15 y^{\prime } x +7 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{3}+x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x +\left (x^{4}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-2 y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +7\right ) y^{\prime }+2 \left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x -18 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x -8 y = 0
\] |
[_erf] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+4\right ) y = 0
\] |
[[_Bessel, _modified]] |
✓ |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \sin \left (x \right )+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -x y = x^{2}+2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}y^{\prime \prime }+\left (x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )+\sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = \cos \left (x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -x y = x^{3}+x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+2 y^{\prime } x -x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-9 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }+y = \frac {1}{x}
\] |
[[_linear, ‘class A‘]] |
✗ |
|
|
\[
{}y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_linear, ‘class A‘]] |
✗ |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✗ |
|
|
\[
{}y^{\prime \prime } = \frac {1}{x}
\] |
[[_2nd_order, _quadrature]] |
✗ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{x}
\] |
[[_2nd_order, _missing_y]] |
✗ |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{a \cos \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +\left (3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +3\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}-3\right ) y^{\prime \prime }-2 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+\frac {8}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (2 x^{2}+\frac {5}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}3 x y^{\prime \prime }-\left (x -2\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x^{2}+2\right ) y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\frac {3 y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Hermite] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }-k y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime }-2 y = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {2 y}{2 x -1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x -3\right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x -1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\frac {y}{x -1} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }-3 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }-5 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\lambda y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\lambda y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } \sin \left (x \right )-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
|
|
\[
{}y^{\prime }+\cos \left (y\right ) = 0
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}{\mathrm e}^{3 x} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+\frac {2 y}{x^{2}+4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {\left (1+{\mathrm e}^{x}\right ) y}{1-{\mathrm e}^{x}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+{\mathrm e}^{2 x} y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x -y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-3 y^{\prime } x +\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y \ln \left (x \right ) = 0
\] |
[_Titchmarsh] |
✓ |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\sqrt {x^{2}+1}\, y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \sin \left (x \right )+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{x +2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\frac {y}{1-x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x +2}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } x +\left (4 x^{3}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-11 y^{\prime }+30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (3 x +2\right ) y^{\prime \prime }+3 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}\left (1+3 x \right ) y^{\prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Hermite] |
✓ |
|
|
\[
{}\left (2 x^{2}+2\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (y^{2}-1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\cos \left (x \right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}5 x y^{\prime \prime }+8 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-k^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +k \left (k +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\] |
[_Laguerre] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}3 x y^{\prime \prime }+11 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
|
|
\[
{}y^{\prime } = \frac {y-x}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } \sin \left (x \right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\ln \left (x \right ) y^{\prime \prime }-\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime \prime }+x \sin \left (y\right ) = 0
\] |
[NONE] |
✗ |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = x^{2} y-y^{\prime }
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}+x y
\] |
[‘y=_G(x,y’)‘] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime }-n y = 0
\] |
[_separable] |
✓ |
|
|
\[
{}9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✗ |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +n^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
|
|
\[
{}\left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (\cos \left (2 x \right )-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
|
|
\[
{}y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✗ |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime \prime }+4 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+y^{\prime } x +y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
|