|
# |
ODE |
CAS classification |
Solved? |
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\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+36 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}36 x^{2} y^{\prime \prime }+60 y^{\prime } x +\left (9 x^{3}-5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+24 y^{\prime } x +\left (144 x^{3}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-12 y^{\prime } x +\left (15+16 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x -2 \left (-x^{5}+14\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (\sqrt {x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = x^{3} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y = 8 x^{{5}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y = x^{{7}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y = 3 x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {t^{2} y}{4} = f \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y x = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{2 x} y = n^{2} y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y}{4 x} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {x +1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (9 x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 y x = 4
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y x = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\left (x -\frac {4}{x}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 y^{\prime } x +\left (x^{6}-36\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }-y x -x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-y x -x^{2}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 \left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}y^{\prime \prime }-c \,x^{a} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left ({\mathrm e}^{2 x}-v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+a \,{\mathrm e}^{b x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}4 y^{\prime \prime }+9 y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x \left (y^{\prime \prime }+y\right )-\cos \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+l x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-y a \,x^{3} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-y x -{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a \,x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+v y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{\operatorname {a1}} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+a y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}a x y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{2}-v \left (v -1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{k}-b \left (b -1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-v^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-v^{2}+x^{2}\right ) y-f \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (l \,x^{2}-v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (a \,x^{m}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (a x -b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (a \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (a^{2} x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (-v^{2}+x^{2}+1\right ) y-f \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x -\left (2 x^{3}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{m}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (4 a^{2} x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-v^{2}+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (a \,x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+\left (4 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 y^{\prime } x -\left (4 x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {a y}{x^{4}}
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {y^{\prime }}{x}-\frac {y}{x^{4}}
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime } = -\frac {2 y^{\prime }}{x}-\frac {a^{2} y}{x^{4}}
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime } = \frac {y^{\prime }}{x}-\frac {a y}{x^{6}}
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-a \,x^{n} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{n} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-n \left (n +1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+n \left (n +1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (a \,x^{3}+\frac {5}{16}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\left (n +\frac {1}{2}\right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\left (n +\frac {1}{2}\right )^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (\nu ^{2}+x^{2}\right ) y = 0
\] |
[[_Bessel, _modified]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -\left (a^{2} x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (b^{2} x^{2}+a \left (a +1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 a x y^{\prime }+\left (-b^{2} x^{2}+a \left (a +1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{n}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{4} y^{\prime \prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{6} y^{\prime \prime }-x^{5} y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{2 a x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-y x = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-\frac {1}{25}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_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)]‘]] |
✓ |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = -t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {6+x}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +4 \left (x^{4}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|