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# |
ODE |
ODE classification |
Solved? |
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\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 72 x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y = 8 x^{{4}/{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+36 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 72 x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y = 8 x^{{4}/{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+4 y^{\prime } t +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +\frac {5 y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+7 y^{\prime } t +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } t +{\mathrm e}^{-t^{2}} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+2 y^{\prime } t +\frac {y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }-5 y^{\prime } t +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 t^{2} y^{\prime \prime }-8 y^{\prime } t +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+5 y^{\prime } t +13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y = 4 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+7 y^{\prime } t +5 y = t
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 2 x^{2}+2
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{{5}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 2 x^{4} \sin \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+2 y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-5 y^{\prime } t +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+2 y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = \ln \left (x^{2}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 1-x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 4 x +\sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +3 y = \left (x -1\right ) \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +y = 9 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{4} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 4 \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = \cos \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 9 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +5 y = 8 x \ln \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{4} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y = 4 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +25 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = x^{2}+2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y = \frac {5 \ln \left (x \right )}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = 8 x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x -\frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = \ln \left (x +1\right )^{2}+x -1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {x +1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \sec \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{2}+2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 \pi y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-3 y^{\prime } t +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -c^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 2 x^{3}-x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 y \csc \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \tan \left (x \right )+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime } \sin \left (x \right )-2 \cos \left (x \right )^{3} y = 2 \cos \left (x \right )^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \tan \left (x \right )+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \tan \left (x \right )-\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \sin \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {a f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+b f \left (x \right )^{2 a} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-y a \,x^{3} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y-a \,x^{2} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +a y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y-3 x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-x^{5} \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{4}+x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y-\sin \left (x \right ) x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +a y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (27 x^{2}+4\right ) y^{\prime \prime }+27 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y = 0
\] |
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (a \,x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (x +a \right ) \left (x +b \right )}-\frac {\left (a -b \right ) y}{4 \left (x +a \right )^{2} \left (x +b \right )}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {2 y^{\prime }}{x}-\frac {a^{2} y}{x^{4}}
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}-1}+\frac {a^{2} y}{\left (x^{2}-1\right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (2 x^{2}+a \right ) y^{\prime }}{x \left (x^{2}+a \right )}-\frac {b y}{x^{2} \left (x^{2}+a \right )}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -a \,x^{2 a -1} x^{-2 a} y^{\prime }-b^{2} x^{-2 a} y
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {y^{\prime }}{x \ln \left (x \right )}+\ln \left (x \right )^{2} y
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}+\frac {y}{\sin \left (x \right )^{2}}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+n y^{\prime }+b \,x^{1-2 n} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +n^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (a \,x^{2}+b \right ) y^{\prime \prime }+a x y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (2 a x +x^{2}+b \right ) y^{\prime \prime }+\left (x +a \right ) y^{\prime }-m^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+d y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \left (2-k \right ) x^{2}+b \left (1-k \right ) x -c k \right ) y^{\prime }+\lambda \,x^{k +1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+2 a x \left (a \,x^{2}+b \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x \left (x^{2 n}+a \right ) y^{\prime \prime }+\left (x^{2 n}+a -a n \right ) y^{\prime }-b^{2} x^{2 n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (a^{2} {\mathrm e}^{2 \lambda x}+b \right ) y^{\prime \prime }-b \lambda y^{\prime }-a^{2} \lambda ^{2} k^{2} {\mathrm e}^{2 \lambda x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 \left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+a \lambda \,{\mathrm e}^{\lambda x} y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \tan \left (x \right )+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y^{\prime } x +10 y = 3 x^{4}+6 x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 4 x -6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 4 \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 2 x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 4 \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y = -6 x^{3}+4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }+x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\frac {\lambda y}{x} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\frac {\lambda y}{x} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}-\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 2 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-y \csc \left (x \right )^{2} = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = t^{7}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = -3 x -\frac {3}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +29 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -25 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 10 x +12
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 22 x +24
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 4 x^{2}+2 x +3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = \frac {5}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +y = \frac {50}{x^{3}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 85 \cos \left (2 \ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y = 4 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \sqrt {x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 12 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 3 \sqrt {x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = \frac {1}{x^{2}+1}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-12 y^{\prime } x +42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-12 y^{\prime } t +42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}3 t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }-9 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-2 y^{\prime } x +20 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +36 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-5 y^{\prime } t +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_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]] |
✓ |
|
|
\[
{}5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 8 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = x \left (6-\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 2 \ln \left (x \right )^{2}+12 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {\alpha \left (\alpha +1\right ) \mu ^{2} y}{-x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +17 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 3 x^{2}+2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y = 4 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+7 y^{\prime } t +5 y = t
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime } = y
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }+x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = \frac {1}{x}
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y = x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 y \csc \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y = x^{5}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y = x^{2} \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } \tan \left (x \right )+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +m^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-y \sin \left (x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
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\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {a^{2} y}{-x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
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\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 8 x^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
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\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x = m^{2} y
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
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\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
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\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
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\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
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\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {y \csc \left (x \right )^{2}}{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
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\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
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\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
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\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime } \sin \left (x \right )-2 \cos \left (x \right )^{3} y = 2 \cos \left (x \right )^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
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\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 4 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
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\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|