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# |
ODE |
CAS 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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = x^{2}-1
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x -3 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = x^{2}-1
\] |
[[_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]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t -3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+7 y^{\prime } t +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2} \ln \left (x \right )
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 2 \left (t -1\right ) {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} \sin \left (x \right ) y^{\prime \prime }-4 x \left (\cos \left (x \right ) x +\sin \left (x \right )\right ) y^{\prime }+\left (2 \cos \left (x \right ) x +3 \sin \left (x \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (2 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 2 x^{2}+2
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a -1\right ) x y^{\prime }+a^{2} y = x^{a +1}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = x^{{3}/{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+2 \left (x +3\right ) y = x^{4} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 2 \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \left (x +1\right ) y^{\prime }+\left (2 x +3\right ) y = x^{{5}/{2}} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = -2 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+5 y^{\prime } t -5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t -2 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-5 y^{\prime } t +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+5 y^{\prime } t -5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+5 y^{\prime } t -2 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+5 y^{\prime } t -5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 y^{\prime } t -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = \ln \left (x^{2}\right )
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 4 \ln \left (x \right )
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = \frac {x^{2}}{\ln \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k}
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = x^{2}+2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = \ln \left (x \right )
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
\] |
[[_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]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = \frac {1}{x}
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 6 x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (-2 x +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x +x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (\sin \left (x \right ) x +\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = \frac {-x^{2}+1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x -y = x^{2}+2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{2}+2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+y^{\prime } x -y = \cos \left (\frac {1}{x}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = x +\frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y = x \left (1-\ln \left (x \right )\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right )
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = \left (x^{2}-1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (1-x \right )^{2}
\] |
[[_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]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {2}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 2 x^{3}-x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+y x = x^{m +1}
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{4} y^{\prime }-x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (f \left (x \right ) x +2\right ) y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y-a \,x^{2} = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y-\sin \left (x \right ) x -\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x -5 y-x^{2} \ln \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{4}+x^{2} = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (2+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+5 y^{\prime } x -y-\ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y = 0
\] |
[_Gegenbauer] |
✓ |
|
|
\[
{}\left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }-x^{2} y^{\prime }+y x -\ln \left (x \right )^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {2 \left (x -2\right ) y^{\prime }}{x \left (x -1\right )}+\frac {2 \left (x +1\right ) y}{x^{2} \left (x -1\right )}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {y^{\prime }}{x +1}-\frac {\left (1+3 x \right ) y}{4 x^{2} \left (x +1\right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}-\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {\left (x^{2}-2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (x^{2}-2\right ) y}{x^{2} \left (x^{2}-1\right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (a \left (a +1\right )-a \,x^{2} \left (a +3\right )\right ) y}{x^{2} \left (x^{2}-1\right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {y^{\prime }}{x^{4}}+\frac {y}{x^{5}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {y^{\prime }}{x \left (\ln \left (x \right )-1\right )}-\frac {y}{x^{2} \left (\ln \left (x \right )-1\right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {x \sin \left (x \right ) y^{\prime }}{\cos \left (x \right ) x -\sin \left (x \right )}+\frac {\sin \left (x \right ) y}{\cos \left (x \right ) x -\sin \left (x \right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {\left (\sin \left (x \right ) x^{2}-2 \cos \left (x \right ) x \right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-\sin \left (x \right ) x \right ) y}{x^{2} \cos \left (x \right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {x y^{\prime }}{f \left (x \right )}+\frac {y}{f \left (x \right )}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }-\left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+\left (c -1\right ) \left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{3}+b \right ) y^{\prime }+a \left (b -1\right ) x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime }+\left (d -1\right ) \left (a \,x^{2}+b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+2\right ) y^{\prime }+a \,x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+a \left (b -1\right ) x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (c -1\right ) \left (a \,x^{n -1}+b \,x^{m -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (a \,x^{n}+b \right ) y^{\prime }+b \left (a \,x^{n}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} \left (a x +b \right ) y^{\prime \prime }-2 x \left (a x +2 b \right ) y^{\prime }+2 \left (a x +3 b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+y x = x
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (1-x \right )^{2}
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }-t x^{\prime }+2 x = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = \left (2 x +1\right )^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 10 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\frac {\left (1+t \right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }+x = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (x +2\right ) y}{x^{2} \left (x +1\right )} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = t^{7}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = -3 x -\frac {3}{x}
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-11 y^{\prime } x +36 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 6 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 64 x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y = \left (x +1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y = \frac {10}{x}
\] |
[[_2nd_order, _exact, _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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 18 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x -2 y = 10 x^{2}
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{\left (x +1\right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{x}
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -16 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}2 t^{2} y^{\prime \prime }-3 y^{\prime } t -3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}3 t^{2} y^{\prime \prime }-5 y^{\prime } t -3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+7 y^{\prime } t -7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}3 t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-y^{\prime } t +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+3 y^{\prime } t +y = \ln \left (t \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+y^{\prime } t +4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y = 2 \ln \left (t \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-y^{\prime } t +y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = \frac {1}{x^{5}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 2 x
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = \ln \left (x \right )
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = x \left (6-\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = -\frac {16 \ln \left (x \right )}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y = x^{2}-2 x +2
\] |
[[_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]] |
✓ |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1-x \cot \left (x \right )\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x -6 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +17 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y = x
\] |
[[_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]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+y^{\prime } t -y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = g \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2} \ln \left (x \right )
\] |
[[_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]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x -5 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = \left (x^{2}-1\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (1-x \right )^{2}
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = \frac {1}{x}
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y = x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y = \left (x +1\right )^{2}
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{m}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\] |
[[_2nd_order, _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]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+y x = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y = x \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -y = f \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 2 \ln \left (x \right )
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y = x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{m}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y = \left (x +1\right )^{2}
\] |
[[_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]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y = x^{2} \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}\left (-b \,x^{2}+a x \right ) y^{\prime \prime }+2 a y^{\prime }+2 b y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+y x = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -y = X
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (1-x \right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = -4 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}-y+y^{\prime } x = \left (x -1\right ) \left (y^{\prime \prime }-x +1\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (x^{2}+a \right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 8 x^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y = x \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 2 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{\left (1-x \right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\] |
[[_2nd_order, _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]] |
✓ |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y = x \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}\left (\sin \left (x \right ) x +\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|