Number of problems in this table is 1303
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = 1+x^{2}+y^{2}+y^{4} x^{2} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.565 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.497 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
7.641 |
|
|
\[ {}x \ln \left (x \right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.007 |
|
|
\[ {}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right ) \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.103 |
|
|
\[ {}t \left (-1+t \right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 y t^{2} = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.114 |
|
|
\[ {}t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.428 |
|
|
\[ {}\left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-t y^{\prime }+y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.586 |
|
|
\[ {}t^{2} \left (3+t \right ) y^{\prime \prime \prime }-3 t \left (2+t \right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.665 |
|
|
\[ {}y^{\prime } = \frac {y+{\mathrm e}^{x}}{x^{2}+y^{2}} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.785 |
|
|
\[ {}y^{\prime } = \tan \left (x y\right ) \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.138 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{\ln \left (x y\right )} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.182 |
|
|
\[ {}y^{\prime } = \left (x^{2}+y^{2}\right ) y^{\frac {1}{3}} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.733 |
|
|
\[ {}y^{\prime } = \ln \left (1+x^{2}+y^{2}\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.883 |
|
|
\[ {}y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.715 |
|
|
\[ {}y^{\prime } = \left (x^{2}+y^{2}\right )^{2} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.569 |
|
|
\[ {}2 x^{2}+8 x y+y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
1.431 |
|
|
\[ {}y \sin \left (x y\right )+x y^{2} \cos \left (x y\right )+\left (x \sin \left (x y\right )+x y^{2} \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
53.93 |
|
|
\[ {}3 x^{2} \cos \left (x \right ) y-x^{3} y^{2} \sin \left (x \right )+4 x +\left (8 y-x^{4} \sin \left (x \right ) y\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
52.588 |
|
|
\[ {}2 x y+y^{2}+\left (2 x y+x^{2}-2 x y^{2}-2 x y^{3}\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
33.105 |
|
|
\[ {}3 x^{2} y^{3}-y^{2}+y+\left (-x y+2 x \right ) y^{\prime } = 0 \] |
1 |
0 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
2.23 |
|
|
\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\left (6 x -8\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.8 |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.225 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = {\mathrm e}^{2 x} \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
1.861 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime }+\left (\sin \left (x \right )-\cos \left (x \right )\right ) y = {\mathrm e}^{-x} \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
3.821 |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (-1+x \right )^{3} y = \left (-1+x \right )^{3} {\mathrm e}^{x} \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
2.296 |
|
|
\[ {}y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.07 |
|
|
\[ {}y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.27 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.707 |
|
|
\[ {}x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
1.437 |
|
|
\[ {}\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y = 0 \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.782 |
|
|
\[ {}y-x^{2} \sqrt {x^{2}-y^{2}}-x y^{\prime } = 0 \] |
1 |
0 |
0 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
2.97 |
|
|
\[ {}\left (x \tan \left (y\right )^{2}-x \right ) y^{\prime } = 2 x^{2}+\tan \left (y\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
6.686 |
|
|
\[ {}1+x y \left (1+x y^{2}\right ) y^{\prime } = 0 \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
N/A |
1.826 |
|
|
\[ {}y^{\prime }+y \ln \left (y\right ) \tan \left (x \right ) = 2 y \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.003 |
|
|
\[ {}1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2} = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
4.369 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x y-1\right ) y^{\prime } = y \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
9.173 |
|
|
\[ {}\frac {y^{\prime \prime }}{y}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {2 a \coth \left (2 x a \right ) y^{\prime }}{y} = 2 a^{2} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.431 |
|
|
\[ {}2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} = \sin \left (x \right ) \] |
1 |
0 |
2 |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
0.589 |
|
|
\[ {}y^{2} \left (x^{2}+1\right )+y+\left (2 x y+1\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.912 |
|
|
\[ {}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.05 |
|
|
\[ {}x^{2}+y^{3}+y = \left (x^{3} y^{2}-x \right ) y^{\prime } \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
1.843 |
|
|
\[ {}2 y^{4} x -y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
1.056 |
|
|
\[ {}x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
1.203 |
|
|
\[ {}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \] |
1 |
0 |
0 |
[_Chini] |
✗ |
N/A |
0.779 |
|
|
\[ {}y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.296 |
|
|
\[ {}y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.158 |
|
|
\[ {}y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right ) = 0 \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.875 |
|
|
\[ {}y^{\prime } = \tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.905 |
|
|
\[ {}y^{\prime } = \left (1+\sin \left (y\right ) \cos \left (x \right )\right ) \tan \left (y\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.441 |
|
|
\[ {}y^{\prime }+f \left (x \right )+g \left (x \right ) \tan \left (y\right ) = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.06 |
|
|
\[ {}y^{\prime } = x^{m -1} y^{-n +1} f \left (a \,x^{m}+b y^{n}\right ) \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.194 |
|
|
\[ {}2 y^{\prime } = 2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
22.05 |
|
|
\[ {}x y^{\prime } = y+x \sqrt {x^{2}+y^{2}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.05 |
|
|
\[ {}x y^{\prime } = y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.285 |
|
|
\[ {}x y^{\prime } = \sin \left (x -y\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.537 |
|
|
\[ {}x y^{\prime }+n y = f \left (x \right ) g \left (x^{n} y\right ) \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.086 |
|
|
\[ {}x^{2} y^{\prime } = \sec \left (y\right )+3 x \tan \left (y\right ) \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.119 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right ) = x \left (x^{2}+1\right ) \cos \left (y\right )^{2} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.553 |
|
|
\[ {}x^{3} y^{\prime } = \cos \left (y\right ) \left (\cos \left (y\right )-2 x^{2} \sin \left (y\right )\right ) \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.839 |
|
|
\[ {}x^{k} y^{\prime } = a \,x^{m}+b y^{n} \] |
1 |
0 |
0 |
[_Chini] |
✗ |
N/A |
0.528 |
|
|
\[ {}y y^{\prime }+x^{3}+y = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.399 |
|
|
\[ {}y y^{\prime }+f \left (x \right ) = g \left (x \right ) y \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.362 |
|
|
\[ {}y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right ) = 0 \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
1.201 |
|
|
\[ {}\left (\tan \left (x \right ) \sec \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right ) = 0 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
6.388 |
|
|
\[ {}\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0 \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.106 |
|
|
\[ {}x \left (y+a \right ) y^{\prime }+b x +c y = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.438 |
|
|
\[ {}\left (a +x \left (x +y\right )\right ) y^{\prime } = b \left (x +y\right ) y \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.633 |
|
|
\[ {}\left (1-x^{2} y\right ) y^{\prime }-1+x y^{2} = 0 \] |
1 |
0 |
3 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.747 |
|
|
\[ {}x^{7} y y^{\prime } = 2 x^{2}+2+5 x^{3} y \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.408 |
|
|
\[ {}\left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
1.832 |
|
|
\[ {}\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (x +y\right )^{2} y^{2} = 0 \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
1.139 |
|
|
\[ {}\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime } = y^{3} \csc \left (x \right ) \sec \left (x \right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
37.644 |
|
|
\[ {}x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime } = 6 y^{3} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
N/A |
1.036 |
|
|
\[ {}\left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (-x^{2}+y^{2}+a \right ) = 0 \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
1.15 |
|
|
\[ {}\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3} = 0 \] |
1 |
0 |
3 |
[_rational] |
✗ |
N/A |
1.039 |
|
|
\[ {}\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+\left (1+y^{4}\right ) y = 0 \] |
1 |
0 |
3 |
[_rational] |
✗ |
N/A |
1.309 |
|
|
\[ {}f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{1+m}+h \left (x \right ) y^{n} = 0 \] |
1 |
0 |
1 |
[_Bernoulli] |
✗ |
N/A |
1.502 |
|
|
\[ {}x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = y \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.405 |
|
|
\[ {}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right ) \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.323 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y = 0 \] |
2 |
0 |
1 |
[_rational] |
✗ |
N/A |
1.644 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.108 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+x \left (x^{2}+x y-2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y = 0 \] |
2 |
0 |
0 |
[_rational] |
✗ |
N/A |
7.028 |
|
|
\[ {}\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2} = 0 \] |
2 |
0 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
143.288 |
|
|
\[ {}x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0 \] |
2 |
0 |
3 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
6.466 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-x y = 0 \] |
2 |
0 |
0 |
[_rational] |
✗ |
N/A |
233.874 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 x a +y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.564 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a -y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
8.827 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.385 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +x^{2} a +\left (1-a \right ) y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
3.305 |
|
|
\[ {}\left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
4.385 |
|
|
\[ {}2 y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-1+x^{2}+y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
74.107 |
|
|
\[ {}\left (-b +a \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
3.382 |
|
|
\[ {}x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0 \] |
2 |
0 |
9 |
[_rational] |
✗ |
N/A |
7.855 |
|
|
\[ {}9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0 \] |
2 |
0 |
9 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.399 |
|
|
\[ {}{y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y} = 0 \] |
3 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
104.449 |
|
|
\[ {}x {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0 \] |
3 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
315.692 |
|
|
\[ {}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0 \] |
3 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
175.365 |
|
|
\[ {}y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0 \] |
3 |
0 |
10 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
134.116 |
|
|
\[ {}{y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 x y^{2} y^{\prime }-16 y^{3} = 0 \] |
4 |
0 |
3 |
[[_homogeneous, ‘class G‘]] |
✗ |
N/A |
1.309 |
|
|
\[ {}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0 \] |
4 |
0 |
5 |
[[_1st_order, _with_linear_symmetries]] |
✗ |
N/A |
2.131 |
|
|
\[ {}x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2} \] |
6 |
0 |
0 |
[_rational] |
✗ |
N/A |
15.077 |
|
|
\[ {}\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y \] |
0 |
0 |
2 |
[_dAlembert] |
✗ |
N/A |
1.551 |
|
|
\[ {}y y^{\prime } = x +y^{2}-y^{2} {y^{\prime }}^{2} \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
3.847 |
|
|
\[ {}\left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime } = y-x^{2} \sqrt {x^{2}-y^{2}} \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
2.7 |
|
|
\[ {}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (y+1\right ) y^{\prime } = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.03 |
|
|
\[ {}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.575 |
|
|
\[ {}s^{2}+s^{\prime } = \frac {s+1}{s t} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
0.42 |
|
|
\[ {}x^{\prime }+x t = {\mathrm e}^{x} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.414 |
|
|
\[ {}x x^{\prime }+x t^{2} = \sin \left (t \right ) \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.865 |
|
|
\[ {}y y^{\prime }+2 x = 5 y^{3} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
0.389 |
|
|
\[ {}2 x +y^{2}-\cos \left (x +y\right )-\left (2 x y-\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
57.155 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y = 0 \] |
1 |
0 |
1 |
[_Laguerre] |
✗ |
N/A |
0.618 |
|
|
\[ {}2 x y+\left (3 y+2 x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.399 |
|
|
\[ {}x -2 \sin \left (y\right )+3+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
3.741 |
|
|
\[ {}\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y = 0 \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.86 |
|
|
\[ {}4 x^{2} y y^{\prime } = 3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3} \] |
1 |
0 |
4 |
[_rational] |
✗ |
N/A |
1.793 |
|
|
\[ {}\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.174 |
|
|
\[ {}\left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right ) = x \] |
1 |
1 |
3 |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
N/A |
0.0 |
|
|
\[ {}3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right ) = -\frac {2}{x} \] |
1 |
1 |
3 |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime } = {\mathrm e}^{2 x} \] |
1 |
1 |
2 |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.764 |
|
|
\[ {}y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.249 |
|
|
\[ {}y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+{\mathrm e}^{x} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.732 |
|
|
\[ {}x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x} \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
10.455 |
|
|
\[ {}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
76.833 |
|
|
\[ {}3 {y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }-y^{\prime \prime } {y^{\prime }}^{2} = 0 \] |
1 |
0 |
2 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{2} y y^{\prime \prime } = x^{2} {y^{\prime }}^{2}-y^{2} \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.096 |
|
|
\[ {}a y^{\prime \prime } y^{\prime \prime \prime } = \sqrt {1+{y^{\prime \prime }}^{2}} \] |
1 |
0 |
4 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}\left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.339 |
|
|
\[ {}\left (-x^{2}+1\right ) \eta ^{\prime \prime }-\left (1+x \right ) \eta ^{\prime }+\left (k +1\right ) \eta = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.397 |
|
|
\[ {}-y+x y^{\prime } = x \sqrt {x^{2}-y^{2}}\, y^{\prime } \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.316 |
|
|
\[ {}y^{\prime \prime \prime \prime }-k^{4} y = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_x]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime }-x y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.27 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.876 |
|
|
\[ {}x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y} \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
16.67 |
|
|
\[ {}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (x \right )^{2} y y^{\prime } = 0 \] |
1 |
0 |
0 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
45.073 |
|
|
\[ {}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.807 |
|
|
\[ {}x y y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3} \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.144 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime } = y+x \,{\mathrm e}^{y} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.541 |
|
|
\[ {}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0 \] |
4 |
0 |
5 |
[[_1st_order, _with_linear_symmetries]] |
✗ |
N/A |
3.405 |
|
|
\[ {}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
N/A |
0.094 |
|
|
\[ {}y^{\prime } = \sqrt {1-x^{2}-y^{2}} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.629 |
|
|
\[ {}y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.566 |
|
|
\[ {}y y^{\prime \prime } = x \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.053 |
|
|
\[ {}y^{2} y^{\prime \prime } = x \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.06 |
|
|
\[ {}3 y y^{\prime \prime } = \sin \left (x \right ) \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.128 |
|
|
\[ {}y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.066 |
|
|
\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.597 |
|
|
\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.446 |
|
|
\[ {}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.733 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.956 |
|
|
\[ {}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.598 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.187 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.58 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.812 |
|
|
\[ {}y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.347 |
|
|
\[ {}y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.845 |
|
|
\[ {}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.947 |
|
|
\[ {}y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.062 |
|
|
\[ {}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = x \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.071 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.071 |
|
|
\[ {}{y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4} \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
12.38 |
|
|
\[ {}y^{\prime } = \frac {x y+3 x -2 y+6}{x y-3 x -2 y+6} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.535 |
|
|
\[ {}{y^{\prime \prime }}^{2}+y^{\prime }+y = 0 \] |
2 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.286 |
|
|
\[ {}y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2} = 0 \] |
1 |
0 |
1 |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.104 |
|
|
\[ {}y^{\prime \prime }+\left (2 x +\sin \left (x \right )\right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2} = 0 \] |
1 |
0 |
1 |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.483 |
|
|
\[ {}y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (y^{2}+3\right ) {y^{\prime }}^{2} = 0 \] |
1 |
0 |
1 |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.112 |
|
|
\[ {}10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0 \] |
1 |
0 |
1 |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.521 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right ) \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
2.789 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.097 |
|
|
\[ {}y^{\prime \prime \prime }-x y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.19 |
|
|
\[ {}y^{\prime }+a \phi ^{\prime }\left (x \right ) y^{3}+6 a \phi \left (x \right ) y^{2}+\frac {\left (2 a +1\right ) y \phi ^{\prime \prime }\left (x \right )}{\phi ^{\prime }\left (x \right )}+2+2 a = 0 \] |
1 |
0 |
0 |
[_Abel] |
✗ |
N/A |
0.239 |
|
|
\[ {}y^{\prime }-f \left (x \right )^{-n +1} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0 \] |
1 |
0 |
1 |
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.73 |
|
|
\[ {}y^{\prime }-a^{n} f \left (x \right )^{-n +1} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0 \] |
1 |
0 |
1 |
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.378 |
|
|
\[ {}y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right ) = 0 \] |
1 |
0 |
0 |
[_Chini] |
✗ |
N/A |
1.478 |
|
|
\[ {}y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.91 |
|
|
\[ {}y^{\prime }-\frac {y-x^{2} \sqrt {x^{2}-y^{2}}}{x y \sqrt {x^{2}-y^{2}}+x} = 0 \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
3.517 |
|
|
\[ {}y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.742 |
|
|
\[ {}y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
3.526 |
|
|
\[ {}y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1 = 0 \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.924 |
|
|
\[ {}y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1 = 0 \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.215 |
|
|
\[ {}y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right ) = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
4.063 |
|
|
\[ {}y^{\prime }-\tan \left (x y\right ) = 0 \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.944 |
|
|
\[ {}y^{\prime }-x^{a -1} y^{-b +1} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right ) = 0 \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.996 |
|
|
\[ {}y^{\prime }-\frac {y a f \left (x^{c} y\right )+c \,x^{a} y^{b}}{x b f \left (x^{c} y\right )-x^{a} y^{b}} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
3.453 |
|
|
\[ {}x y^{\prime }-x \sqrt {x^{2}+y^{2}}-y = 0 \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.835 |
|
|
\[ {}x y^{\prime }-x \left (y-x \right ) \sqrt {x^{2}+y^{2}}-y = 0 \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
2.317 |
|
|
\[ {}x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right ) = 0 \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.674 |
|
|
\[ {}x y^{\prime }-\sin \left (x -y\right ) = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.619 |
|
|
\[ {}x y^{\prime }+a y-f \left (x \right ) g \left (x^{a} y\right ) = 0 \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.882 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2} = 0 \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
4.674 |
|
|
\[ {}f \left (x \right ) y^{\prime }+g \left (x \right ) s \left (y\right )+h \left (x \right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.99 |
|
|
\[ {}y y^{\prime }+x^{3}+y = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.529 |
|
|
\[ {}y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n} = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.325 |
|
|
\[ {}y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a = 0 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.085 |
|
|
\[ {}y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right ) = 0 \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
2.21 |
|
|
\[ {}\left (y+g \left (x \right )\right ) y^{\prime }-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right ) = 0 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
9.226 |
|
|
\[ {}x y y^{\prime }-y^{2}+x y+x^{3}-2 x^{2} = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.738 |
|
|
\[ {}x \left (y+a \right ) y^{\prime }+b y+c x = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.77 |
|
|
\[ {}\left (B x y+A \,x^{2}+x a +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+\alpha x +\beta y+\gamma = 0 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
6.216 |
|
|
\[ {}\left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1 = 0 \] |
1 |
0 |
3 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.338 |
|
|
\[ {}\left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8 = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.757 |
|
|
\[ {}x \left (x y+x^{4}-1\right ) y^{\prime }-y \left (x y-x^{4}-1\right ) = 0 \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.035 |
|
|
\[ {}\left (x^{n \left (n +1\right )} y-1\right ) y^{\prime }+2 \left (n +1\right )^{2} x^{n -1} \left (x^{n^{2}} y^{2}-1\right ) = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.551 |
|
|
\[ {}\left (g_{1} \left (x \right ) y+g_{0} \left (x \right )\right ) y^{\prime }-f_{1} \left (x \right ) y-f_{2} \left (x \right ) y^{2}-f_{3} \left (x \right ) y^{3}-f_{0} \left (x \right ) = 0 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
48.582 |
|
|
\[ {}\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (x +y\right )^{2} y^{2} = 0 \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
2.048 |
|
|
\[ {}\left (\frac {y^{2}}{b}+\frac {x^{2}}{a}\right ) \left (y y^{\prime }+x \right )+\frac {\left (-b +a \right ) \left (y y^{\prime }-x \right )}{a +b} = 0 \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
2.642 |
|
|
\[ {}\left (2 a y^{3}+3 a x y^{2}-b \,x^{3}+c \,x^{2}\right ) y^{\prime }-a y^{3}+c y^{2}+3 b \,x^{2} y+2 b \,x^{3} = 0 \] |
1 |
0 |
3 |
[_rational] |
✗ |
N/A |
2.221 |
|
|
\[ {}\left (x^{2} y^{3}+x y\right ) y^{\prime }-1 = 0 \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
N/A |
1.332 |
|
|
\[ {}\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+y^{5}+y = 0 \] |
1 |
0 |
3 |
[_rational] |
✗ |
N/A |
2.097 |
|
|
\[ {}y^{\prime } \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right ) = 0 \] |
1 |
0 |
2 |
unknown |
✗ |
N/A |
41.768 |
|
|
\[ {}y^{\prime } \cos \left (y\right )+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3} = 0 \] |
1 |
0 |
2 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
48.569 |
|
|
\[ {}x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right ) = 0 \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
33.409 |
|
|
\[ {}f \left (x^{c} y\right ) \left (b x y^{\prime }-a \right )-x^{a} y^{b} \left (x y^{\prime }+c y\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
3.075 |
|
|
\[ {}{y^{\prime }}^{2}+y^{2}-f \left (x \right )^{2} = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.067 |
|
|
\[ {}{y^{\prime }}^{2}+2 f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right ) = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
14.407 |
|
|
\[ {}\left (x y^{\prime }+a \right )^{2}-2 a y+x^{2} = 0 \] |
2 |
0 |
1 |
[_rational] |
✗ |
N/A |
4.225 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
6.124 |
|
|
\[ {}\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x y+x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
26.482 |
|
|
\[ {}x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x = 0 \] |
2 |
0 |
3 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
8.06 |
|
|
\[ {}{\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y} = 0 \] |
2 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
12.216 |
|
|
\[ {}\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
11.382 |
|
|
\[ {}\operatorname {d0} \left (x \right ) {y^{\prime }}^{2}+2 \operatorname {b0} \left (x \right ) y y^{\prime }+\operatorname {c0} \left (x \right ) y^{2}+2 \operatorname {d0} \left (x \right ) y^{\prime }+2 \operatorname {e0} \left (x \right ) y+\operatorname {f0} \left (x \right ) = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
77.711 |
|
|
\[ {}\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0 \] |
2 |
0 |
0 |
[_rational] |
✗ |
N/A |
2.563 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0 \] |
2 |
0 |
0 |
[_rational] |
✗ |
N/A |
24.905 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 x a +y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
5.074 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a y^{2}+b x +c = 0 \] |
2 |
0 |
2 |
[_rational] |
✗ |
N/A |
5.374 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
5.46 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +x^{2} a +\left (1-a \right ) y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
7.128 |
|
|
\[ {}\left (y^{2}-2 x a +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0 \] |
2 |
0 |
2 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
7.22 |
|
|
\[ {}\left (-b +a \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2} = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
6.755 |
|
|
\[ {}\left (a y^{2}+b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2} = 0 \] |
2 |
0 |
3 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
13.713 |
|
|
\[ {}\left (\operatorname {b2} y+\operatorname {a2} x +\operatorname {c2} \right )^{2} {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {b0} y+\operatorname {a0} +\operatorname {c0} = 0 \] |
2 |
0 |
0 |
[_rational] |
✗ |
N/A |
90.787 |
|
|
\[ {}x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y = 0 \] |
2 |
0 |
9 |
[_rational] |
✗ |
N/A |
15.87 |
|
|
\[ {}x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (y-x \right ) y^{\prime }-y^{2} \left (x^{2} y-1\right ) = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
30.803 |
|
|
\[ {}\left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right ) = 0 \] |
2 |
0 |
2 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
12.389 |
|
|
\[ {}\left (y^{4}+x^{2} y^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2} = 0 \] |
2 |
0 |
4 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
8.423 |
|
|
\[ {}9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2} = 0 \] |
2 |
0 |
9 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
7.985 |
|
|
\[ {}x^{2} \left (y^{4} x^{2}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (-x^{2}+y^{2}\right ) y^{\prime }-y^{2} \left (x^{4} y^{2}-1\right ) = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
26.609 |
|
|
\[ {}\left (a \left (x^{2}+y^{2}\right )^{\frac {3}{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (x^{2}+y^{2}\right )^{\frac {3}{2}}-y^{2} = 0 \] |
2 |
0 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✗ |
N/A |
39.219 |
|
|
\[ {}{y^{\prime }}^{2} \sin \left (y\right )+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4} = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
99.033 |
|
|
\[ {}{y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+y^{4} x^{2}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6} = 0 \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
21.569 |
|
|
\[ {}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0 \] |
3 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
146.769 |
|
|
\[ {}{y^{\prime }}^{4}-4 y \left (x y^{\prime }-2 y\right )^{2} = 0 \] |
4 |
0 |
3 |
[[_homogeneous, ‘class G‘]] |
✗ |
N/A |
1.073 |
|
|
\[ {}x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y = 0 \] |
0 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.272 |
|
|
\[ {}f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0 \] |
2 |
0 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✗ |
N/A |
6.225 |
|
|
\[ {}a \,x^{n} f \left (y^{\prime }\right )+x y^{\prime }-y = 0 \] |
0 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.537 |
|
|
\[ {}\left (-y+x y^{\prime }\right )^{n} f \left (y^{\prime }\right )+y g \left (y^{\prime }\right )+x h \left (y^{\prime }\right ) = 0 \] |
0 |
0 |
0 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
2.117 |
|
|
\[ {}f \left (x {y^{\prime }}^{2}\right )+2 x y^{\prime }-y = 0 \] |
0 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.347 |
|
|
\[ {}f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y = 0 \] |
0 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
0.781 |
|
|
\[ {}y^{\prime } f \left (x y y^{\prime }-y^{2}\right )-x^{2} y^{\prime }+x y = 0 \] |
0 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.613 |
|
|
\[ {}\phi \left (f \left (x , y, y^{\prime }\right ), g \left (x , y, y^{\prime }\right )\right ) = 0 \] |
0 |
0 |
0 |
[NONE] |
✗ |
N/A |
1.004 |
|
|
\[ {}y^{\prime } = \frac {1+2 F \left (\frac {4 x^{2} y+1}{4 x^{2}}\right ) x}{2 x^{3}} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
0.969 |
|
|
\[ {}y^{\prime } = \frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
0.977 |
|
|
\[ {}y^{\prime } = -\frac {\left (x^{2} a -2 F \left (y+\frac {a \,x^{4}}{8}\right )\right ) x}{2} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.083 |
|
|
\[ {}y^{\prime } = F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
0.955 |
|
|
\[ {}y^{\prime } = \frac {F \left (\frac {y}{\sqrt {x^{2}+1}}\right ) x}{\sqrt {x^{2}+1}} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.4 |
|
|
\[ {}y^{\prime } = \frac {\left (x^{\frac {3}{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.075 |
|
|
\[ {}y^{\prime } = \frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y} \] |
1 |
0 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
0.993 |
|
|
\[ {}y^{\prime } = \frac {x}{-y+F \left (x^{2}+y^{2}\right )} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.041 |
|
|
\[ {}y^{\prime } = \frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y} \] |
1 |
0 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.084 |
|
|
\[ {}y^{\prime } = \frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.298 |
|
|
\[ {}y^{\prime } = \frac {F \left (y^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.175 |
|
|
\[ {}y^{\prime } = \frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y} \] |
1 |
0 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
0.985 |
|
|
\[ {}y^{\prime } = \frac {F \left (\frac {1+x y^{2}}{x}\right )}{y x^{2}} \] |
1 |
0 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
0.931 |
|
|
\[ {}y^{\prime } = \frac {-x +F \left (x^{2}+y^{2}\right )}{y} \] |
1 |
0 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.027 |
|
|
\[ {}y^{\prime } = \frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y} \] |
1 |
0 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.099 |
|
|
\[ {}y^{\prime } = \frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}} \] |
1 |
0 |
2 |
[NONE] |
✗ |
N/A |
1.191 |
|
|
\[ {}y^{\prime } = \frac {2 F \left (y+\ln \left (2 x +1\right )\right ) x +F \left (y+\ln \left (2 x +1\right )\right )-2}{2 x +1} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.044 |
|
|
\[ {}y^{\prime } = \frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y} \] |
1 |
0 |
2 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
1.141 |
|
|
\[ {}y^{\prime } = -\left (-{\mathrm e}^{-x^{2}}+x^{2} {\mathrm e}^{-x^{2}}-F \left (y-\frac {x^{2} {\mathrm e}^{-x^{2}}}{2}\right )\right ) x \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.217 |
|
|
\[ {}y^{\prime } = \frac {2 y+F \left (\frac {y}{x^{2}}\right ) x^{3}}{x} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
0.956 |
|
|
\[ {}y^{\prime } = \frac {-3 x^{2} y+F \left (x^{3} y\right )}{x^{3}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
0.961 |
|
|
\[ {}y^{\prime } = \frac {-2 x -y+F \left (x \left (x +y\right )\right )}{x} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.066 |
|
|
\[ {}y^{\prime } = \frac {x +y+F \left (-\frac {-y+x \ln \left (x \right )}{x}\right ) x^{2}}{x} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.165 |
|
|
\[ {}y^{\prime } = \frac {x \left (a -1\right ) \left (1+a \right )}{y+F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right ) a^{2}-F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right )} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.178 |
|
|
\[ {}y^{\prime } = \frac {F \left (\frac {\left (3+y\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{3 y}\right ) x y^{2} {\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.406 |
|
|
\[ {}y^{\prime } = \frac {\left (y+1\right ) \left (\left (y-\ln \left (y+1\right )-\ln \left (x \right )\right ) x +1\right )}{y x} \] |
1 |
0 |
2 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.148 |
|
|
\[ {}y^{\prime } = \frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )} \] |
1 |
0 |
1 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
1.25 |
|
|
\[ {}y^{\prime } = \frac {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.931 |
|
|
\[ {}y^{\prime } = \frac {x}{y+\sqrt {x^{2}+1}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
2.449 |
|
|
\[ {}y^{\prime } = \frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.5 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.121 |
|
|
\[ {}y^{\prime } = -\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \] |
1 |
0 |
1 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
0.998 |
|
|
\[ {}y^{\prime } = \left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.984 |
|
|
\[ {}y^{\prime } = \frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.066 |
|
|
\[ {}y^{\prime } = \frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.386 |
|
|
\[ {}y^{\prime } = \frac {\left (-y^{2}+4 x a \right )^{2}}{y} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
1.089 |
|
|
\[ {}y^{\prime } = -\frac {x^{2} \left (x a -2 \sqrt {a \left (a \,x^{4}+8 y\right )}\right )}{2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.37 |
|
|
\[ {}y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{\frac {5}{2}} y} \] |
1 |
0 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.277 |
|
|
\[ {}y^{\prime } = -\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
2.175 |
|
|
\[ {}y^{\prime } = \frac {2 a +x \sqrt {-y^{2}+4 x a}}{y} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.353 |
|
|
\[ {}y^{\prime } = \frac {2 a +x^{2} \sqrt {-y^{2}+4 x a}}{y} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.323 |
|
|
\[ {}y^{\prime } = -\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
2.103 |
|
|
\[ {}y^{\prime } = \frac {\left (-2 y^{\frac {3}{2}}+3 \,{\mathrm e}^{x}\right )^{2} {\mathrm e}^{x}}{4 \sqrt {y}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
1.619 |
|
|
\[ {}y^{\prime } = \frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.197 |
|
|
\[ {}y^{\prime } = \frac {\left (1+x y^{2}\right )^{2}}{y x^{4}} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
1.087 |
|
|
\[ {}y^{\prime } = \frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
3.261 |
|
|
\[ {}y^{\prime } = \frac {x +1+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3} \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.501 |
|
|
\[ {}y^{\prime } = \frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 x +2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.516 |
|
|
\[ {}y^{\prime } = \frac {y+\sqrt {x^{2}+y^{2}}\, x^{2}}{x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.227 |
|
|
\[ {}y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.201 |
|
|
\[ {}y^{\prime } = \frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.624 |
|
|
\[ {}y^{\prime } = \frac {y+x^{3} \sqrt {x^{2}+y^{2}}}{x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.397 |
|
|
\[ {}y^{\prime } = \frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.526 |
|
|
\[ {}y^{\prime } = \frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3+3 x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.567 |
|
|
\[ {}y^{\prime } = \frac {1}{x \left (x y^{2}+1+x \right ) y} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
N/A |
0.954 |
|
|
\[ {}y^{\prime } = \frac {\left (-y^{2}+4 x a \right )^{3}}{\left (-y^{2}+4 x a -1\right ) y} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
1.386 |
|
|
\[ {}y^{\prime } = \frac {2 x a +2 a +x^{3} \sqrt {-y^{2}+4 x a}}{\left (1+x \right ) y} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
6.14 |
|
|
\[ {}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{1+x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.255 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.58 |
|
|
\[ {}y^{\prime } = \frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.619 |
|
|
\[ {}y^{\prime } = \frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (1+x \right ) y^{2}} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
3.016 |
|
|
\[ {}y^{\prime } = \frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (1+x \right ) y^{2}} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.8 |
|
|
\[ {}y^{\prime } = \frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (1+x \right )} \] |
1 |
0 |
2 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
1.342 |
|
|
\[ {}y^{\prime } = \frac {\left (2 y^{\frac {3}{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{\frac {3}{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.519 |
|
|
\[ {}y^{\prime } = \frac {-x^{2}-x -x a -a +2 x^{3} \sqrt {x^{2}+2 x a +a^{2}+4 y}}{2 x +2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
1.704 |
|
|
\[ {}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{1+x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.288 |
|
|
\[ {}y^{\prime } = \frac {x \left (-1+x -2 x y+2 x^{3}\right )}{x^{2}-y} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.118 |
|
|
\[ {}y^{\prime } = \frac {x +y^{4}-2 x^{2} y^{2}+x^{4}}{y} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
1.194 |
|
|
\[ {}y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{\frac {5}{2}} \left (a y^{2}+b \,x^{2}+a \right ) y} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.455 |
|
|
\[ {}y^{\prime } = -\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (1+x \right )} \] |
1 |
0 |
2 |
unknown |
✗ |
N/A |
9.466 |
|
|
\[ {}y^{\prime } = -\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
1.939 |
|
|
\[ {}y^{\prime } = \frac {x}{-y+x^{4}+2 x^{2} y^{2}+y^{4}} \] |
1 |
0 |
3 |
[_rational] |
✗ |
N/A |
1.28 |
|
|
\[ {}y^{\prime } = -\frac {i \left (i x +x^{4}+2 x^{2} y^{2}+y^{4}\right )}{y} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
1.878 |
|
|
\[ {}y^{\prime } = \frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
1.149 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (1+x \right )} \] |
1 |
0 |
2 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
43.079 |
|
|
\[ {}y^{\prime } = \frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
1.426 |
|
|
\[ {}y^{\prime } = \frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (1+x \right )} \] |
1 |
0 |
1 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
1.496 |
|
|
\[ {}y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
2.324 |
|
|
\[ {}y^{\prime } = \frac {\left (1+x y^{2}\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y} \] |
1 |
0 |
5 |
[_rational] |
✗ |
N/A |
1.355 |
|
|
\[ {}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.484 |
|
|
\[ {}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.325 |
|
|
\[ {}y^{\prime } = -\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
2.345 |
|
|
\[ {}y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 y^{4} x^{2}} \] |
1 |
0 |
3 |
[_rational] |
✗ |
N/A |
1.35 |
|
|
\[ {}y^{\prime } = \frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
1.279 |
|
|
\[ {}y^{\prime } = \frac {x y+y+x \sqrt {x^{2}+y^{2}}}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.931 |
|
|
\[ {}y^{\prime } = \frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (1+x \right )} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.211 |
|
|
\[ {}y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
3.549 |
|
|
\[ {}y^{\prime } = \frac {\left (1+x +y\right ) y}{\left (2 y^{3}+y+x \right ) \left (1+x \right )} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
2.457 |
|
|
\[ {}y^{\prime } = -\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
2.216 |
|
|
\[ {}y^{\prime } = \frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.939 |
|
|
\[ {}y^{\prime } = \frac {-\sin \left (2 y\right ) x -\sin \left (2 y\right )+\cos \left (2 y\right ) x^{4}+x^{4}}{2 x \left (1+x \right )} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
11.148 |
|
|
\[ {}y^{\prime } = \frac {x y+y+x^{4} \sqrt {x^{2}+y^{2}}}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.475 |
|
|
\[ {}y^{\prime } = \frac {-\sin \left (2 y\right ) x -\sin \left (2 y\right )+x \cos \left (2 y\right )+x}{2 x \left (1+x \right )} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
7.264 |
|
|
\[ {}y^{\prime } = -\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
3.126 |
|
|
\[ {}y^{\prime } = \frac {x^{3} {\mathrm e}^{y}+x^{4}+{\mathrm e}^{y} y-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+x y-\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
3.885 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
34.612 |
|
|
\[ {}y^{\prime } = \frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
3.765 |
|
|
\[ {}y^{\prime } = \frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )} \] |
1 |
0 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
2.653 |
|
|
\[ {}y^{\prime } = \frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
4.293 |
|
|
\[ {}y^{\prime } = \frac {\left (x -y\right )^{3} \left (x +y\right )^{3} x}{\left (-y^{2}+x^{2}-1\right ) y} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
2.537 |
|
|
\[ {}y^{\prime } = \frac {-2 \cos \left (y\right )+x^{3} \cos \left (2 y\right ) \ln \left (x \right )+x^{3} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
48.375 |
|
|
\[ {}y^{\prime } = -\frac {2 x}{3}+\sqrt {x^{2}+3 y}+x^{2} \sqrt {x^{2}+3 y}+x^{3} \sqrt {x^{2}+3 y} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
2.898 |
|
|
\[ {}y^{\prime } = \frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+\ln \left (x \right ) x^{2}}{2 \sin \left (y\right ) \ln \left (x \right ) x} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
47.844 |
|
|
\[ {}y^{\prime } = \frac {\left (3 x y^{2}+x +3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x \left (1+x \right )} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
2.453 |
|
|
\[ {}y^{\prime } = -\frac {-y+x^{3} \sqrt {x^{2}+y^{2}}-x^{2} \sqrt {x^{2}+y^{2}}\, y}{x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.288 |
|
|
\[ {}y^{\prime } = \frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.35 |
|
|
\[ {}y^{\prime } = \frac {2 a +\sqrt {-y^{2}+4 x a}+x^{2} \sqrt {-y^{2}+4 x a}+x^{3} \sqrt {-y^{2}+4 x a}}{y} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
25.428 |
|
|
\[ {}y^{\prime } = \frac {\left (1+x +y\right ) y}{\left (y^{4}+y^{3}+y^{2}+x \right ) \left (1+x \right )} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
2.424 |
|
|
\[ {}y^{\prime } = -\frac {-y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y}{x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.367 |
|
|
\[ {}y^{\prime } = \frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x \left (1+x \right )} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.02 |
|
|
\[ {}y^{\prime } = -\frac {1}{-\left (y^{3}\right )^{\frac {2}{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{\frac {1}{3}} x} \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
2.438 |
|
|
\[ {}y^{\prime } = \frac {y \left (x -y\right ) \left (y+1\right )}{x \left (x y+x -y\right )} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
3.013 |
|
|
\[ {}y^{\prime } = -\frac {1}{-\ln \left (x \right ) \left (y^{3}\right )^{\frac {2}{3}}-\textit {\_F1} \left (y^{3}+3 \,\operatorname {expIntegral}_{1}\left (-\ln \left (x \right )\right )\right ) \ln \left (x \right ) \left (y^{3}\right )^{\frac {1}{3}}} \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
3.037 |
|
|
\[ {}y^{\prime } = \frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{\frac {3}{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{\frac {3}{2}} b \,x^{2}+a^{\frac {5}{2}} y^{4}}{a \,x^{2} y} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
4.005 |
|
|
\[ {}y^{\prime } = \frac {y \left (x +y\right ) \left (y+1\right )}{x \left (x y+x +y\right )} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
2.26 |
|
|
\[ {}y^{\prime } = \frac {3 x^{3}+\sqrt {-9 x^{4}+4 y^{3}}+x^{2} \sqrt {-9 x^{4}+4 y^{3}}+x^{3} \sqrt {-9 x^{4}+4 y^{3}}}{y^{2}} \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
6.203 |
|
|
\[ {}y^{\prime } = \frac {1}{-x +\left (\frac {1}{y}+1\right ) x +\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \] |
1 |
0 |
2 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.708 |
|
|
\[ {}y^{\prime } = \frac {x}{2}+\frac {1}{2}+\sqrt {x^{2}+2 x +1-4 y}+x^{2} \sqrt {x^{2}+2 x +1-4 y}+x^{3} \sqrt {x^{2}+2 x +1-4 y} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
3.155 |
|
|
\[ {}y^{\prime } = \frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
4.316 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
3.218 |
|
|
\[ {}y^{\prime } = \frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right ) \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
5.882 |
|
|
\[ {}y^{\prime } = \frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+x^{2} \ln \left (x \right )^{2}+2 x^{2} \ln \left (y\right ) \ln \left (x \right )+x^{2} \ln \left (y\right )^{2}\right )}{x} \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
3.891 |
|
|
\[ {}y^{\prime } = \frac {y \left (\ln \left (y\right )-1+\ln \left (x \right )+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}\right )}{x} \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
3.783 |
|
|
\[ {}y^{\prime } = -\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \] |
1 |
0 |
2 |
[NONE] |
✗ |
N/A |
3.537 |
|
|
\[ {}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
3.575 |
|
|
\[ {}y^{\prime } = -\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \] |
1 |
0 |
2 |
[NONE] |
✗ |
N/A |
3.542 |
|
|
\[ {}y^{\prime } = -\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
2.957 |
|
|
\[ {}y^{\prime } = \frac {y+x \sqrt {x^{2}+y^{2}}+x^{3} \sqrt {x^{2}+y^{2}}+x^{4} \sqrt {x^{2}+y^{2}}}{x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.476 |
|
|
\[ {}y^{\prime } = \left (\frac {\ln \left (y-1\right ) y}{\left (1-y\right ) \ln \left (x \right ) x}-\frac {\ln \left (y-1\right )}{\left (1-y\right ) \ln \left (x \right ) x}-f \left (x \right )\right ) \left (1-y\right ) \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.328 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+\sqrt {x^{2}+2 x a +a^{2}+4 y}+x^{2} \sqrt {x^{2}+2 x a +a^{2}+4 y}+x^{3} \sqrt {x^{2}+2 x a +a^{2}+4 y} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
N/A |
3.785 |
|
|
\[ {}y^{\prime } = \frac {-x +1-2 y+3 x^{2}-2 x^{2} y+2 x^{4}+x^{3}-2 x^{3} y+2 x^{5}}{x^{2}-y} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
2.652 |
|
|
\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x +x^{3}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
4.373 |
|
|
\[ {}y^{\prime } = -\frac {-x y-y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
4.088 |
|
|
\[ {}y^{\prime } = \frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
2.915 |
|
|
\[ {}y^{\prime } = -\frac {-x y-y+\sqrt {x^{2}+y^{2}}\, x^{2}-x \sqrt {x^{2}+y^{2}}\, y}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.691 |
|
|
\[ {}y^{\prime } = \frac {\left (a^{3}+y^{4} a^{3}+2 y^{2} a^{2} b \,x^{2}+a \,x^{4} b^{2}+y^{6} a^{3}+3 y^{4} a^{2} b \,x^{2}+3 y^{2} a \,b^{2} x^{4}+b^{3} x^{6}\right ) x}{a^{\frac {7}{2}} y} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
5.099 |
|
|
\[ {}y^{\prime } = -\frac {\left (-1-y^{4}+2 x^{2} y^{2}-x^{4}-y^{6}+3 y^{4} x^{2}-3 x^{4} y^{2}+x^{6}\right ) x}{y} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
2.701 |
|
|
\[ {}y^{\prime } = -\frac {i \left (32 i x +64+64 y^{4}+32 x^{2} y^{2}+4 x^{4}+64 y^{6}+48 y^{4} x^{2}+12 x^{4} y^{2}+x^{6}\right )}{128 y} \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
8.035 |
|
|
\[ {}y^{\prime } = -\frac {\left (-8-8 y^{3}+24 y^{\frac {3}{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{\frac {9}{2}}+36 y^{3} {\mathrm e}^{x}-54 y^{\frac {3}{2}} {\mathrm e}^{2 x}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
5.087 |
|
|
|
||||||||
|
\[ {}y^{\prime } = \frac {x}{-y+1+y^{4}+2 x^{2} y^{2}+x^{4}+y^{6}+3 y^{4} x^{2}+3 x^{4} y^{2}+x^{6}} \] |
1 |
0 |
7 |
[_rational] |
✗ |
N/A |
2.939 |
|
|
\[ {}y^{\prime } = \frac {y^{2} \left (-2 y+2 x^{2}+2 x^{2} y+y x^{4}\right )}{x^{3} \left (x^{2}-y+x^{2} y\right )} \] |
1 |
0 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
3.371 |
|
|
\[ {}y^{\prime } = -\frac {i \left (i x +1+x^{4}+2 x^{2} y^{2}+y^{4}+x^{6}+3 x^{4} y^{2}+3 y^{4} x^{2}+y^{6}\right )}{y} \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
7.515 |
|
|
\[ {}y^{\prime } = \frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 x^{2} a +512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \] |
1 |
0 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
4.528 |
|
|
\[ {}y^{\prime } = \frac {x +1+y^{4}-2 x^{2} y^{2}+x^{4}+y^{6}-3 y^{4} x^{2}+3 x^{4} y^{2}-x^{6}}{y} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
2.694 |
|
|
\[ {}y^{\prime } = \frac {\left (-108 y x^{\frac {3}{2}}+18 x^{\frac {9}{2}}-108 x^{\frac {3}{2}}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216} \] |
1 |
0 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
31.148 |
|
|
\[ {}y^{\prime } = \frac {32 x^{5} y+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \] |
1 |
0 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
4.204 |
|
|
\[ {}y^{\prime } = \frac {-x y^{2}+x^{3}-x -y^{6}+3 y^{4} x^{2}-3 x^{4} y^{2}+x^{6}}{\left (-y^{2}+x^{2}-1\right ) y} \] |
1 |
0 |
4 |
[_rational] |
✗ |
N/A |
3.136 |
|
|
\[ {}y^{\prime } = \frac {x \left (1+x^{2}+y^{2}\right )}{-y^{3}-x^{2} y-y+y^{6}+3 y^{4} x^{2}+3 x^{4} y^{2}+x^{6}} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
3.5 |
|
|
\[ {}y^{\prime } = \frac {4 x \left (a -1\right ) \left (1+a \right )}{4 y+a^{2} y^{4}-2 a^{4} y^{2} x^{2}+4 y^{2} a^{2} x^{2}+a^{6} x^{4}-3 a^{4} x^{4}+3 a^{2} x^{4}-y^{4}-2 x^{2} y^{2}-x^{4}} \] |
1 |
0 |
3 |
[_rational] |
✗ |
N/A |
4.1 |
|
|
\[ {}y^{\prime } = \frac {x^{3}+y^{4} x^{3}+2 x^{2} y^{2}+x +x^{3} y^{6}+3 y^{4} x^{2}+3 x y^{2}+1}{x^{5} y} \] |
1 |
0 |
8 |
[_rational] |
✗ |
N/A |
3.374 |
|
|
\[ {}y^{\prime } = \frac {y \left (\ln \left (y\right ) x +\ln \left (y\right )-x -1+x \ln \left (x \right )+\ln \left (x \right )+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
12.056 |
|
|
\[ {}y^{\prime } = \frac {y \left (x \ln \left (x \right )+\ln \left (x \right )+\ln \left (y\right ) x +\ln \left (y\right )-x -1+x \ln \left (x \right )^{2}+2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}\right )}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
4.967 |
|
|
\[ {}y^{\prime } = \frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 y^{4} x +32 y^{6} x^{2}+2+24 x y^{2}+96 y^{4} x^{2}+128 x^{3} y^{6}} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
3.741 |
|
|
\[ {}y^{\prime } = \frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 y^{5} x +y^{5}+2+24 x y^{2}+96 y^{4} x^{2}+128 x^{3} y^{6}} \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
3.885 |
|
|
\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x \right ) {\mathrm e}^{\frac {y}{x}}}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
4.066 |
|
|
\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x \left (1+x \right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.941 |
|
|
\[ {}y^{\prime } = \frac {\left (27 y^{3}+27 \,{\mathrm e}^{3 x^{2}} y+18 \,{\mathrm e}^{3 x^{2}} y^{2}+3 y^{3} {\mathrm e}^{3 x^{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}}+27 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y+9 \,{\mathrm e}^{\frac {9 x^{2}}{2}} y^{2}+{\mathrm e}^{\frac {9 x^{2}}{2}} y^{3}\right ) {\mathrm e}^{3 x^{2}} x \,{\mathrm e}^{-\frac {9 x^{2}}{2}}}{243 y} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
35.108 |
|
|
\[ {}y^{\prime } = \frac {-2 y-2 \ln \left (2 x +1\right )-2+2 x y^{3}+y^{3}+6 y^{2} \ln \left (2 x +1\right ) x +3 y^{2} \ln \left (2 x +1\right )+6 y \ln \left (2 x +1\right )^{2} x +3 y \ln \left (2 x +1\right )^{2}+2 \ln \left (2 x +1\right )^{3} x +\ln \left (2 x +1\right )^{3}}{\left (2 x +1\right ) \left (y+\ln \left (2 x +1\right )+1\right )} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
35.34 |
|
|
\[ {}y^{\prime } = \frac {y \ln \left (x \right ) x +\ln \left (x \right ) x^{2}-2 x y-x^{2}-y^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x \left (-y+x \ln \left (x \right )-x \right )} \] |
1 |
0 |
2 |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
4.381 |
|
|
\[ {}y^{\prime } = \frac {\left (-8 \,{\mathrm e}^{-x^{2}} y+4 x^{2} {\mathrm e}^{-2 x^{2}}-8 \,{\mathrm e}^{-x^{2}}+8 x^{2} {\mathrm e}^{-x^{2}} y-4 x^{4} {\mathrm e}^{-2 x^{2}}+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}-6 y x^{4} {\mathrm e}^{-2 x^{2}}+x^{6} {\mathrm e}^{-3 x^{2}}\right ) x}{-8 y+4 x^{2} {\mathrm e}^{-x^{2}}-8} \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
42.027 |
|
|
\[ {}y^{\prime } = -\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 x y+60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
4.053 |
|
|
\[ {}y^{\prime } = -\frac {-y+\sqrt {x^{2}+y^{2}}\, x^{2}-x \sqrt {x^{2}+y^{2}}\, y+x^{4} \sqrt {x^{2}+y^{2}}-x^{3} \sqrt {x^{2}+y^{2}}\, y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
5.291 |
|
|
\[ {}y^{\prime } = \frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+x \ln \left (x \right )^{2}+2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x} \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
5.59 |
|
|
\[ {}y^{\prime } = \frac {-150 x^{3} y+60 x^{6}+350 x^{\frac {7}{2}}-150 x^{3}-125 y \sqrt {x}+250 x -125 \sqrt {x}-125 y^{3}+150 x^{3} y^{2}+750 y^{2} \sqrt {x}-60 y x^{6}-600 y x^{\frac {7}{2}}-1500 x y+8 x^{9}+120 x^{\frac {13}{2}}+600 x^{4}+1000 x^{\frac {3}{2}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \] |
1 |
0 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
N/A |
50.033 |
|
|
\[ {}y^{\prime } = \frac {4 x \left (a -1\right ) \left (1+a \right ) \left (-y^{2}+a^{2} x^{2}-x^{2}-2\right )}{-4 y^{3}+4 a^{2} x^{2} y-4 x^{2} y-8 y-a^{2} y^{6}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 y^{4} x^{2}+3 x^{4} y^{2}+x^{6}} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
7.815 |
|
|
\[ {}y^{\prime } = -\frac {8 x \left (a -1\right ) \left (1+a \right )}{8+2 x^{4}+2 y^{4}+3 x^{4} y^{2}-8 y+x^{6}-8 y^{2} a^{2} x^{2}-2 a^{2} y^{4}+4 a^{4} y^{2} x^{2}+y^{6}-8 a^{2}+4 x^{2} y^{2}+3 y^{4} x^{2}-6 y^{4} a^{2} x^{2}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-2 a^{6} x^{4}+6 a^{4} x^{4}-6 a^{2} x^{4}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}-4 a^{2} x^{6}-a^{2} y^{6}} \] |
1 |
0 |
7 |
[_rational] |
✗ |
N/A |
9.055 |
|
|
\[ {}y^{\prime } = -\frac {1296 y}{216-432 x y-324 x^{2} y^{3}+216 x y^{2}-846 y^{7}-1944 y^{4}-2376 y^{2}+216 x^{3}-1296 y+216 x^{2}-1728 y^{3}-648 x^{2} y+1152 y^{4} x -612 y^{5}-882 y^{6}+594 x y^{6}-126 y^{10}-8 y^{12}-36 y^{11}-315 y^{9}-570 y^{8}+72 y^{8} x +216 y^{7} x -648 x^{2} y^{2}-216 y^{4} x^{2}+1080 y^{5} x +1080 x y^{3}} \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
5.546 |
|
|
\[ {}y^{\prime } = -\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-1296 x y-324 x^{2} y^{3}-1944 x y^{2}+594 y^{7}+2808 y^{4}-1296 y^{2}+216 x^{3}-1296 y+1728 y^{3}-648 x^{2} y-432 y^{4} x +4428 y^{5}+2484 y^{6}+594 x y^{6}-126 y^{10}-8 y^{12}-36 y^{11}-315 y^{9}-18 y^{8}+72 y^{8} x +216 y^{7} x -648 x^{2} y^{2}-216 y^{4} x^{2}+1080 y^{5} x -648 x y^{3}} \] |
1 |
0 |
2 |
[_rational] |
✗ |
N/A |
6.566 |
|
|
\[ {}y^{\prime } = \frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{-x^{2}+y} \] |
1 |
0 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
3.581 |
|
|
\[ {}y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 b \,x^{2}}-1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.934 |
|
|
\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 x}+b \,{\mathrm e}^{x}+c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.497 |
|
|
\[ {}y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.75 |
|
|
\[ {}y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y = 0 \] |
1 |
0 |
1 |
[_ellipsoidal] |
✗ |
N/A |
0.596 |
|
|
\[ {}y^{\prime \prime }+\left (a \cos \left (x \right )^{2}+b \right ) y = 0 \] |
1 |
0 |
1 |
[_ellipsoidal] |
✗ |
N/A |
0.744 |
|
|
\[ {}y^{\prime \prime }-\left (1+2 \tan \left (x \right )^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.596 |
|
|
\[ {}y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
5.163 |
|
|
\[ {}y^{\prime \prime }-\left (n \left (n +1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+B \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.652 |
|
|
\[ {}y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.675 |
|
|
\[ {}y^{\prime \prime }-\left (\frac {p^{\prime \prime \prime \prime }\left (x \right )}{30}+\frac {7 p^{\prime \prime }\left (x \right )}{3}+a p \left (x \right )+b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.05 |
|
|
\[ {}y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.169 |
|
|
\[ {}y^{\prime \prime }+\left (P \left (x \right )+l \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.125 |
|
|
\[ {}y^{\prime \prime }-f \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.112 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.789 |
|
|
\[ {}y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.215 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (n +1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.588 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-n y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.56 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-a y = 0 \] |
1 |
0 |
1 |
[_Hermite] |
✗ |
N/A |
0.576 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+a y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.602 |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }+\left (3 x^{2}+2 n -1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.689 |
|
|
\[ {}y^{\prime \prime }+a x y^{\prime }+b y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.721 |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+\left (c x +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.908 |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.056 |
|
|
\[ {}y^{\prime \prime }+a \,x^{q -1} y^{\prime }+b \,x^{q -2} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.89 |
|
|
\[ {}y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.845 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } \cot \left (x \right )+v \left (v +1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.166 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime } \tan \left (x \right )+b y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.436 |
|
|
\[ {}y^{\prime \prime }+a p^{\prime \prime }\left (x \right ) y^{\prime }+\left (a +b p \left (x \right )-4 n a p \left (x \right )^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.259 |
|
|
\[ {}y^{\prime \prime }+\frac {\left (11 \operatorname {WeierstrassP}\left (x , a , b\right ) \operatorname {WeierstrassPPrime}\left (x , a , b\right )-6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}+\frac {a}{2}\right ) y^{\prime }}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}}+\frac {\left (\operatorname {WeierstrassPPrime}\left (x , a , b\right )^{2}-\operatorname {WeierstrassP}\left (x , a , b\right )^{2} \operatorname {WeierstrassPPrime}\left (x , a , b\right )-\operatorname {WeierstrassP}\left (x , a , b\right ) \left (6 \operatorname {WeierstrassP}\left (x , a , b\right )^{2}-\frac {a}{2}\right )\right ) y}{\operatorname {WeierstrassPPrime}\left (x , a , b\right )+\operatorname {WeierstrassP}\left (x , a , b\right )^{2}} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
86.672 |
|
|
\[ {}y^{\prime \prime }+f \left (x \right ) y^{\prime }+g \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.28 |
|
|
\[ {}y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right )+a \right ) y-g \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.244 |
|
|
\[ {}y^{\prime \prime }+\left (a f \left (x \right )+b \right ) y^{\prime }+\left (c f \left (x \right )+d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.681 |
|
|
\[ {}y^{\prime \prime }-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+2 a \right ) y^{\prime }+\left (\frac {a f^{\prime }\left (x \right )}{f \left (x \right )}+a^{2}-b^{2} f \left (x \right )^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.642 |
|
|
\[ {}y^{\prime \prime }+\frac {f \left (x \right ) f^{\prime \prime \prime }\left (x \right ) y^{\prime }}{f \left (x \right )^{2}+b^{2}}-\frac {a^{2} {f^{\prime }\left (x \right )}^{2} y}{f \left (x \right )^{2}+b^{2}} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.052 |
|
|
\[ {}y^{\prime \prime }-\left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) \left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right )}{f \left (x \right )}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {v^{2} {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.604 |
|
|
\[ {}y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right ) y^{\prime }+\left (\frac {h^{\prime }\left (x \right ) \left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right )}{h \left (x \right )}-\frac {h^{\prime \prime }\left (x \right )}{h \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.644 |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime } \tan \left (x \right )-\left (5 \tan \left (x \right )^{2}+2\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.287 |
|
|
\[ {}a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.168 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.431 |
|
|
\[ {}x y^{\prime \prime }+\left (x +b \right ) y^{\prime }+a y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.125 |
|
|
\[ {}x y^{\prime \prime }+\left (x +a +b \right ) y^{\prime }+a y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.261 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }-a y = 0 \] |
1 |
0 |
1 |
[_Laguerre] |
✗ |
N/A |
0.635 |
|
|
\[ {}x y^{\prime \prime }+\left (b -x \right ) y^{\prime }-a y = 0 \] |
1 |
0 |
1 |
[_Laguerre] |
✗ |
N/A |
1.073 |
|
|
\[ {}x y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }-y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.741 |
|
|
\[ {}x y^{\prime \prime }-\left (-2+3 x \right ) y^{\prime }-\left (2 x -3\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.956 |
|
|
\[ {}x y^{\prime \prime }+\left (x a +b +n \right ) y^{\prime }+n a y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.461 |
|
|
\[ {}x y^{\prime \prime }-\left (a +b \right ) \left (1+x \right ) y^{\prime }+a b x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.168 |
|
|
\[ {}x y^{\prime \prime }+\left (x \left (a +b \right )+m +n \right ) y^{\prime }+\left (a b x +a n +b m \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.511 |
|
|
\[ {}x y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+\left (c x +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.961 |
|
|
\[ {}x y^{\prime \prime }-2 \left (x^{2}-a \right ) y^{\prime }+2 n x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.467 |
|
|
\[ {}2 x y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+a y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.946 |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+a y = 0 \] |
1 |
0 |
1 |
[_Laguerre] |
✗ |
N/A |
0.937 |
|
|
\[ {}5 \left (x a +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (x a +b \right )^{\frac {1}{5}} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.859 |
|
|
\[ {}2 a x y^{\prime \prime }+\left (b x +a \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.209 |
|
|
\[ {}2 a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.21 |
|
|
\[ {}\left (\operatorname {a2} x +\operatorname {b2} \right ) y^{\prime \prime }+\left (\operatorname {a1} x +\operatorname {b1} \right ) y^{\prime }+\left (\operatorname {a0} x +\operatorname {b0} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
9.317 |
|
|
\[ {}x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.433 |
|
|
\[ {}x^{2} y^{\prime \prime }+a y^{\prime }-x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.746 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+a y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.578 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 \left (x +a \right ) y^{\prime }-b \left (b -1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.797 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.231 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x a +b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.969 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x +3\right ) x y^{\prime }-y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.93 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (x +a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.006 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-v \left (v -1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.845 |
|
|
\[ {}x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.274 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2 x a +b \right ) x y^{\prime }+\left (a b x +c \,x^{2}+d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.618 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x a +b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.365 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.682 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2} a +b \right ) x y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.688 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.043 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2 n}+\operatorname {b1} \,x^{n}+\operatorname {c1} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.336 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (a \,x^{\operatorname {a1}}+b \right ) x y^{\prime }+\left (A \,x^{2 \operatorname {a1}}+B \,x^{\operatorname {a1}}+C \,x^{\operatorname {b1}}+\operatorname {DD} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.8 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 x^{2} \tan \left (x \right )-x \right ) y^{\prime }-\left (x \tan \left (x \right )+a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.028 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2} \cot \left (x \right )+x \right ) y^{\prime }+\left (x \cot \left (x \right )+a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.036 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right ) x +f \left (x \right )^{2}-f \left (x \right )+x^{2} a +b x +c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.887 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} f \left (x \right ) y^{\prime }+\left (x^{2} \left (f^{\prime }\left (x \right )+f \left (x \right )^{2}+a \right )-v \left (v -1\right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.888 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x -2 f \left (x \right ) x^{2}\right ) y^{\prime }+\left (x^{2} \left (1+f \left (x \right )^{2}-f^{\prime }\left (x \right )\right )-f \left (x \right ) x -v^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.897 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-v \left (v -1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.931 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
0.739 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {\partial }{\partial x}\operatorname {LegendreP}\left (n , x\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.793 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.514 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-l y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.037 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-v \left (v +1\right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.086 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }-\left (v +2\right ) \left (v -1\right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
375.082 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (v +n +1\right ) \left (v -n \right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.046 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (v -n +1\right ) \left (v +n \right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.001 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.645 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.996 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.974 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-v \left (v +1\right ) y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
0.715 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
1.017 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime }-l y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
1.032 |
|
|
\[ {}x \left (2+x \right ) y^{\prime \prime }+2 \left (n +1+\left (n +1-2 l \right ) x -l \,x^{2}\right ) y^{\prime }+\left (2 l \left (p -n -1\right ) x +2 p l +m \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.912 |
|
|
\[ {}\left (-1+x \right ) \left (-2+x \right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
163.593 |
|
|
\[ {}2 x \left (-1+x \right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (x a +b \right ) y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
0.688 |
|
|
\[ {}2 x \left (-1+x \right ) y^{\prime \prime }+\left (\left (2 v +5\right ) x -2 v -3\right ) y^{\prime }+\left (v +1\right ) y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
0.889 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.18 |
|
|
\[ {}x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (a -1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.006 |
|
|
\[ {}48 x \left (-1+x \right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
2.178 |
|
|
\[ {}144 x \left (-1+x \right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
0.937 |
|
|
\[ {}144 x \left (-1+x \right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
0.765 |
|
|
\[ {}\operatorname {a2} \,x^{2} y^{\prime \prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x \right ) y^{\prime }+\left (\operatorname {a0} \,x^{2}+\operatorname {b0} x +\operatorname {c0} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.572 |
|
|
\[ {}\operatorname {A2} \left (x a +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (x a +b \right ) y^{\prime }+\operatorname {A0} \left (x a +b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.467 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime \prime }+\left (d x +f \right ) y^{\prime }+g y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.107 |
|
|
\[ {}x^{3} y^{\prime \prime }+2 x y^{\prime }-y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.298 |
|
|
\[ {}x^{3} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.477 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 x^{2}+1\right ) y^{\prime }-v \left (v +1\right ) x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.915 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 \left (n +1\right ) x^{2}+2 n +1\right ) y^{\prime }-\left (v -n \right ) \left (v +n +1\right ) x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.099 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }-\left (2 \left (n -1\right ) x^{2}+2 n -1\right ) y^{\prime }+\left (v +n \right ) \left (-v +n -1\right ) x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.049 |
|
|
\[ {}x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-x y = 0 \] |
1 |
0 |
1 |
[[_elliptic, _class_II]] |
✗ |
N/A |
82.461 |
|
|
\[ {}x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+x y = 0 \] |
1 |
0 |
1 |
[[_elliptic, _class_I]] |
✗ |
N/A |
0.746 |
|
|
\[ {}x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2} a +b \right ) y^{\prime }+c x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.424 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (\left (b +a +1\right ) x +\alpha +\beta -1\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (a b x -\alpha \beta \right ) y}{x^{2} \left (-1+x \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.389 |
|
|
\[ {}y^{\prime \prime } = \frac {2 y^{\prime }}{x \left (-2+x \right )}-\frac {y}{x^{2} \left (-2+x \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
78.828 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +\delta \right )-\delta \right ) x +a \gamma \right ) y^{\prime }}{x \left (-1+x \right ) \left (x -a \right )}-\frac {\left (\alpha \beta x -q \right ) y}{x \left (-1+x \right ) \left (x -a \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.026 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )}-\frac {\left (\operatorname {DD} x +E \right ) y}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
5.145 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}+\frac {v \left (v +1\right ) y}{4 x^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.895 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (\left (1+a \right ) x -1\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (\left (a^{2}-b^{2}\right ) x +c^{2}\right ) y}{4 x^{2} \left (-1+x \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.076 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}-\frac {\left (x a +b \right ) y}{4 x \left (-1+x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.802 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (a \left (b +2\right ) x^{2}+\left (c -d +1\right ) x \right ) y^{\prime }}{\left (x a +1\right ) x^{2}}-\frac {\left (a b x -c d \right ) y}{\left (x a +1\right ) x^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.325 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (2 x a +b \right ) y^{\prime }}{x \left (x a +b \right )}-\frac {\left (a v x -b \right ) y}{\left (x a +b \right ) x^{2}}+A x \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
84.643 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left ({\mathrm e}^{\frac {2}{x}}-v^{2}\right ) y}{x^{4}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.317 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {y}{x^{4}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.46 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (-v \left (v +1\right ) x^{2}-n^{2}\right ) y}{x^{2} \left (x^{2}+1\right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.977 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (x^{2} a +a -1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (b \,x^{2}+c \right ) y}{x^{2} \left (x^{2}+1\right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.147 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (x^{2} a +a -2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {b y}{x^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.461 |
|
|
\[ {}y^{\prime \prime } = \frac {\left (2 b c \,x^{c} \left (x^{2}-1\right )+2 \left (a -1\right ) x^{2}-2 a \right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (b^{2} c^{2} x^{2 c} \left (x^{2}-1\right )+b c \,x^{c +2} \left (2 a -c -1\right )-b c \,x^{c} \left (2 a -c +1\right )+x^{2} \left (a \left (a -1\right )-v \left (v +1\right )\right )-a \left (1+a \right )\right ) y}{x^{2} \left (x^{2}-1\right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
5.592 |
|
|
\[ {}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}+1}-\frac {\left (a^{2} \left (x^{2}+1\right )^{2}-n \left (n +1\right ) \left (x^{2}+1\right )+m^{2}\right ) y}{\left (x^{2}+1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.914 |
|
|
\[ {}y^{\prime \prime } = -\frac {a x y^{\prime }}{x^{2}+1}-\frac {b y}{\left (x^{2}+1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.74 |
|
|
\[ {}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (-a^{2}-\lambda \left (x^{2}-1\right )\right ) y}{\left (x^{2}-1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.027 |
|
|
\[ {}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (\left (x^{2}-1\right ) \left (x^{2} a +b x +c \right )-k^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.645 |
|
|
\[ {}y^{\prime \prime } = -\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (-a^{2} \left (x^{2}-1\right )^{2}-n \left (n +1\right ) \left (x^{2}-1\right )-m^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.523 |
|
|
\[ {}y^{\prime \prime } = \frac {2 x \left (2 a -1\right ) y^{\prime }}{x^{2}-1}-\frac {\left (x^{2} \left (2 a \left (2 a -1\right )-v \left (v +1\right )\right )+2 a +v \left (v +1\right )\right ) y}{\left (x^{2}-1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.355 |
|
|
\[ {}y^{\prime \prime } = -\frac {2 x \left (n +1-2 a \right ) y^{\prime }}{x^{2}-1}-\frac {\left (4 a \,x^{2} \left (a -n \right )-\left (x^{2}-1\right ) \left (2 a +\left (v -n \right ) \left (v +n +1\right )\right )\right ) y}{\left (x^{2}-1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.651 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}-\frac {\left (v \left (v +1\right ) \left (-1+x \right )-x \,a^{2}\right ) y}{4 x^{2} \left (-1+x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.017 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}-\frac {\left (-v \left (v +1\right ) \left (-1+x \right )^{2}-4 n^{2} x \right ) y}{4 x^{2} \left (-1+x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.108 |
|
|
\[ {}y^{\prime \prime } = -\frac {b x y^{\prime }}{\left (x^{2}-1\right ) a}-\frac {\left (c \,x^{2}+d x +e \right ) y}{a \left (x^{2}-1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.845 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (3 x^{2}-1\right ) y^{\prime }}{\left (x^{2}-1\right ) x}-\frac {\left (x^{2}-1-\left (2 v +1\right )^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.394 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (\left (1-4 a \right ) x^{2}-1\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (\left (-v^{2}+x^{2}\right ) \left (x^{2}-1\right )^{2}+4 a \left (1+a \right ) x^{4}-2 a \,x^{2} \left (x^{2}-1\right )\right ) y}{x^{2} \left (x^{2}-1\right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.409 |
|
|
\[ {}y^{\prime \prime } = -\left (\frac {1-\operatorname {a1} -\operatorname {b1}}{x -\operatorname {c1}}+\frac {1-\operatorname {a2} -\operatorname {b2}}{x -\operatorname {c2}}+\frac {1-\operatorname {a3} -\operatorname {b3}}{x -\operatorname {c3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {a1} \operatorname {b1} \left (\operatorname {c1} -\operatorname {c3} \right ) \left (\operatorname {c1} -\operatorname {c2} \right )}{x -\operatorname {c1}}+\frac {\operatorname {a2} \operatorname {b2} \left (\operatorname {c2} -\operatorname {c1} \right ) \left (\operatorname {c2} -\operatorname {c3} \right )}{x -\operatorname {c2}}+\frac {\operatorname {a3} \operatorname {b3} \left (\operatorname {c3} -\operatorname {c2} \right ) \left (\operatorname {c3} -\operatorname {c1} \right )}{x -\operatorname {c3}}\right ) y}{\left (x -\operatorname {c1} \right ) \left (x -\operatorname {c2} \right ) \left (x -\operatorname {c3} \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
42.941 |
|
|
\[ {}y^{\prime \prime } = -\left (\frac {\left (1-\operatorname {al1} -\operatorname {bl1} \right ) \operatorname {b1}}{\operatorname {b1} x -\operatorname {a1}}+\frac {\left (1-\operatorname {al2} -\operatorname {bl2} \right ) \operatorname {b2}}{\operatorname {b2} x -\operatorname {a2}}+\frac {\left (1-\operatorname {al3} -\operatorname {bl3} \right ) \operatorname {b3}}{\operatorname {b3} x -\operatorname {a3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {al1} \operatorname {bl1} \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right ) \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right )}{\operatorname {b1} x -\operatorname {a1}}+\frac {\operatorname {al2} \operatorname {bl2} \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right ) \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right )}{\operatorname {b2} x -\operatorname {a2}}+\frac {\operatorname {al3} \operatorname {bl3} \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right ) \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right )}{\operatorname {b3} x -\operatorname {a3}}\right ) y}{\left (\operatorname {b1} x -\operatorname {a1} \right ) \left (\operatorname {b2} x -\operatorname {a2} \right ) \left (\operatorname {b3} x -\operatorname {a3} \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
13.112 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}-\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
12.957 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (a p \,x^{b}+q \right ) y^{\prime }}{x \left (a \,x^{b}-1\right )}-\frac {\left (a r \,x^{b}+s \right ) y}{x^{2} \left (a \,x^{b}-1\right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.974 |
|
|
\[ {}y^{\prime \prime } = \frac {y}{1+{\mathrm e}^{x}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
N/A |
0.138 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (-a^{2} \sinh \left (x \right )^{2}-n \left (n -1\right )\right ) y}{\sinh \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.822 |
|
|
\[ {}y^{\prime \prime } = -\frac {2 n \cosh \left (x \right ) y^{\prime }}{\sinh \left (x \right )}-\left (-a^{2}+n^{2}\right ) y \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.396 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (1+2 n \right ) \cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\left (v +n +1\right ) \left (v -n \right ) y \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.869 |
|
|
\[ {}\cos \left (x \right )^{2} y^{\prime \prime }-\left (a \cos \left (x \right )^{2}+n \left (n -1\right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.911 |
|
|
\[ {}y^{\prime \prime } = \frac {2 y}{\sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.715 |
|
|
\[ {}y^{\prime \prime } = -\frac {a y}{\sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.625 |
|
|
\[ {}\sin \left (x \right )^{2} y^{\prime \prime }-\left (a \sin \left (x \right )^{2}+n \left (n -1\right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.832 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (-a^{2} \cos \left (x \right )^{2}-\left (3-2 a \right ) \cos \left (x \right )-3+3 a \right ) y}{\sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.194 |
|
|
\[ {}\sin \left (x \right )^{2} y^{\prime \prime }-\left (a^{2} \cos \left (x \right )^{2}+b \cos \left (x \right )+\frac {b^{2}}{\left (2 a -3\right )^{2}}+3 a +2\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
5.682 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (-\left (a^{2} b^{2}-\left (1+a \right )^{2}\right ) \sin \left (x \right )^{2}-a \left (1+a \right ) b \sin \left (2 x \right )-a \left (a -1\right )\right ) y}{\sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.829 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (a \cos \left (x \right )^{2}+b \sin \left (x \right )^{2}+c \right ) y}{\sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.32 |
|
|
\[ {}y^{\prime \prime } = -\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.603 |
|
|
\[ {}y^{\prime \prime } = -\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
6.938 |
|
|
\[ {}y^{\prime \prime } = -\frac {b \cos \left (x \right ) y^{\prime }}{\sin \left (x \right ) a}-\frac {\left (c \cos \left (x \right )^{2}+d \cos \left (x \right )+e \right ) y}{a \sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.235 |
|
|
\[ {}y^{\prime \prime } = -\frac {4 \sin \left (3 x \right ) y}{\sin \left (x \right )^{3}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.712 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (4 v \left (v +1\right ) \sin \left (x \right )^{2}-\cos \left (x \right )^{2}+2-4 n^{2}\right ) y}{4 \sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.677 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (-a \cos \left (x \right )^{2} \sin \left (x \right )^{2}-m \left (m -1\right ) \sin \left (x \right )^{2}-n \left (n -1\right ) \cos \left (x \right )^{2}\right ) y}{\cos \left (x \right )^{2} \sin \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.011 |
|
|
\[ {}y^{\prime \prime } = \frac {\phi ^{\prime }\left (x \right ) y^{\prime }}{\phi \left (x \right )-\phi \left (a \right )}-\frac {\left (-n \left (n +1\right ) \left (\phi \left (x \right )-\phi \left (a \right )\right )^{2}+D^{\left (2\right )}\left (\phi \right )\left (a \right )\right ) y}{\phi \left (x \right )-\phi \left (a \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.618 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (\phi \left (x^{3}\right )-\phi \left (x \right ) \phi ^{\prime }\left (x \right )-\phi ^{\prime \prime }\left (x \right )\right ) y^{\prime }}{\phi ^{\prime }\left (x \right )+\phi \left (x \right )^{2}}-\frac {\left ({\phi ^{\prime }\left (x \right )}^{2}-\phi \left (x \right )^{2} \phi ^{\prime }\left (x \right )-\phi \left (x \right ) \phi ^{\prime \prime }\left (x \right )\right ) y}{\phi ^{\prime }\left (x \right )+\phi \left (x \right )^{2}} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.445 |
|
|
\[ {}y^{\prime \prime } = \frac {2 \,\operatorname {JacobiSN}\left (x , k\right ) \operatorname {JacobiCN}\left (x , k\right ) \operatorname {JacobiDN}\left (x , k\right ) y^{\prime }-2 \left (1-2 \left (k^{2}+1\right ) \operatorname {JacobiSN}\left (a , k\right )^{2}+3 k^{2} \operatorname {JacobiSN}\left (a , k\right )^{4}\right ) y}{\operatorname {JacobiSN}\left (x , k\right )^{2}-\operatorname {JacobiSN}\left (a , k\right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
82.612 |
|
|
\[ {}y^{\prime \prime } = -\frac {f^{\prime }\left (x \right ) y^{\prime }}{2 f \left (x \right )}-\frac {g \left (x \right ) y}{f \left (x \right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.392 |
|
|
\[ {}y^{\prime \prime } = -\frac {\left (2 f \left (x \right ) {g^{\prime }\left (x \right )}^{2} g \left (x \right )-\left (g \left (x \right )^{2}-1\right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )\right ) y^{\prime }}{f \left (x \right ) g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )}-\frac {\left (\left (g \left (x \right )^{2}-1\right ) \left (f^{\prime }\left (x \right ) \left (f \left (x \right ) g^{\prime \prime }\left (x \right )+2 f^{\prime }\left (x \right ) g^{\prime }\left (x \right )\right )-f \left (x \right ) f^{\prime \prime }\left (x \right ) g^{\prime }\left (x \right )\right )-\left (2 f^{\prime }\left (x \right ) g \left (x \right )+v \left (v +1\right ) f \left (x \right ) g^{\prime }\left (x \right )\right ) f \left (x \right ) {g^{\prime }\left (x \right )}^{2}\right ) y}{f \left (x \right )^{2} g^{\prime }\left (x \right ) \left (g \left (x \right )^{2}-1\right )} \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.621 |
|
|
\[ {}y^{\prime \prime \prime }+y a \,x^{3}-b x = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.082 |
|
|
\[ {}y^{\prime \prime \prime }-a \,x^{b} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.082 |
|
|
\[ {}y^{\prime \prime \prime }+2 a x y^{\prime }+a y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.122 |
|
|
|
||||||||
|
\[ {}y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-b y a = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.134 |
|
|
\[ {}y^{\prime \prime \prime }+x^{2 c -2} y^{\prime }+\left (c -1\right ) x^{2 c -3} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.083 |
|
|
\[ {}y^{\prime \prime \prime }-3 \left (2 \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+a \right ) y^{\prime }+b y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.088 |
|
|
\[ {}y^{\prime \prime \prime }+\left (-n^{2}+1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }+\frac {\left (\left (-n^{2}+1\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right )-a \right ) y}{2} = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.095 |
|
|
\[ {}y^{\prime \prime \prime }-\left (4 n \left (n +1\right ) \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+a \right ) y^{\prime }-2 n \left (n +1\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.089 |
|
|
\[ {}y^{\prime \prime \prime }+\left (A \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )+a \right ) y^{\prime }+B \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.089 |
|
|
\[ {}y^{\prime \prime \prime }-\left (3 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime }+\left (b +c \operatorname {JacobiSN}\left (z , x\right )^{2}-3 k^{2} \operatorname {JacobiSN}\left (z , x\right ) \operatorname {JacobiCN}\left (z , x\right ) \operatorname {JacobiDN}\left (z , x\right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.093 |
|
|
\[ {}y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.088 |
|
|
\[ {}y^{\prime \prime \prime }+2 f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.086 |
|
|
\[ {}y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.19 |
|
|
\[ {}y^{\prime \prime \prime }+3 a x y^{\prime \prime }+3 a^{2} x^{2} y^{\prime }+a^{3} x^{3} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.191 |
|
|
\[ {}y^{\prime \prime \prime }-\sin \left (x \right ) y^{\prime \prime }-2 y^{\prime } \cos \left (x \right )+y \sin \left (x \right )-\ln \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
N/A |
0.092 |
|
|
\[ {}y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.089 |
|
|
\[ {}y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y\right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.087 |
|
|
\[ {}y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime }+g \left (x \right ) y^{\prime }+\left (f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.093 |
|
|
\[ {}y^{\prime \prime \prime }+3 f \left (x \right ) y^{\prime \prime }+\left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}+4 g \left (x \right )\right ) y^{\prime }+\left (4 f \left (x \right ) g \left (x \right )+2 g^{\prime }\left (x \right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.099 |
|
|
\[ {}27 y^{\prime \prime \prime }-36 n^{2} \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }-2 n \left (n +3\right ) \left (4 n -3\right ) \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.092 |
|
|
\[ {}x y^{\prime \prime \prime }+3 y^{\prime \prime }+x y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.228 |
|
|
\[ {}x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.25 |
|
|
\[ {}x y^{\prime \prime \prime }+\left (a +b \right ) y^{\prime \prime }-x y^{\prime }-a y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.234 |
|
|
\[ {}x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.394 |
|
|
\[ {}x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-f \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
N/A |
0.091 |
|
|
\[ {}2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+a x y-b = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.088 |
|
|
\[ {}2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.362 |
|
|
\[ {}2 x y^{\prime \prime \prime }+3 \left (2 x a +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.424 |
|
|
\[ {}\left (-2+x \right ) x y^{\prime \prime \prime }-\left (-2+x \right ) x y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
N/A |
0.26 |
|
|
\[ {}\left (2 x -1\right ) y^{\prime \prime \prime }-8 x y^{\prime }+8 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.283 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-6 y^{\prime }+a \,x^{2} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.251 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+\left (1+x \right ) y^{\prime \prime }-y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.05 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+\left (4 a^{2} x^{2 a}+1-4 \nu ^{2} a^{2}\right ) y^{\prime } = 4 a^{3} x^{2 a -1} y \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.098 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-3 \left (x -m \right ) x y^{\prime \prime }+\left (2 x^{2}+4 \left (n -m \right ) x +m \left (2 m -1\right )\right ) y^{\prime }-2 n \left (2 x -2 m +1\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.428 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+4 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }+3 x y-f \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.098 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }+6 y^{\prime }+a \,x^{2} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.265 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-3 \left (p +q \right ) x y^{\prime \prime }+3 p \left (3 q +1\right ) y^{\prime }-x^{2} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.262 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (x^{2} a +6 n \right ) y^{\prime }-2 a x y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.267 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-\left (x^{2}-2 x \right ) y^{\prime \prime }-\left (x^{2}+\nu ^{2}-\frac {1}{4}\right ) y^{\prime }+\left (x^{2}-2 x +\nu ^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.452 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (1+x \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.34 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-2 \left (x^{2}-x \right ) y^{\prime \prime }+\left (x^{2}-2 x +\frac {1}{4}-\nu ^{2}\right ) y^{\prime }+\left (\nu ^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.378 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-\left (x^{4}-6 x \right ) y^{\prime \prime }-\left (2 x^{3}-6\right ) y^{\prime }+2 x^{2} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.286 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }-2 x y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.059 |
|
|
\[ {}2 x \left (-1+x \right ) y^{\prime \prime \prime }+3 \left (2 x -1\right ) y^{\prime \prime }+\left (2 x a +b \right ) y^{\prime }+a y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.436 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (-\nu ^{2}+1\right ) x y^{\prime }+\left (a \,x^{3}+\nu ^{2}-1\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.261 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.255 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (a \,x^{2 \nu }+1-\nu ^{2}\right ) x y^{\prime }+\left (b \,x^{3 \nu }+a \left (\nu -1\right ) x^{2 \nu }+\nu ^{2}-1\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.1 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+\left (x^{2}+8\right ) x y^{\prime }-2 \left (x^{2}+4\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.251 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+\left (a \,x^{3}-12\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.246 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 \left (1-a \right ) x^{2} y^{\prime \prime }+\left (4 b^{2} c^{2} x^{2 c +1}+1-4 \nu ^{2} c^{2}+3 a \left (a -1\right ) x \right ) y^{\prime }+\left (4 b^{2} c^{2} \left (c -a \right ) x^{2 c}+a \left (4 \nu ^{2} c^{2}-a^{2}\right )\right ) y = 0 \] |
1 |
0 |
0 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.107 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.277 |
|
|
\[ {}\left (x^{2}+1\right ) x y^{\prime \prime \prime }+3 \left (2 x^{2}+1\right ) y^{\prime \prime }-12 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.233 |
|
|
\[ {}\left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (2+x \right ) y^{\prime \prime }+6 \left (1+x \right ) y^{\prime }-6 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.356 |
|
|
\[ {}2 \left (x -\operatorname {a1} \right ) \left (x -\operatorname {a2} \right ) \left (x -\operatorname {a3} \right ) y^{\prime \prime \prime }+\left (9 x^{2}-6 \left (\operatorname {a1} +\operatorname {a2} +\operatorname {a3} \right ) x +3 \operatorname {a1} \operatorname {a2} +3 \operatorname {a1} \operatorname {a3} +3 \operatorname {a2} \operatorname {a3} \right ) y^{\prime \prime }-2 \left (\left (n^{2}+n -3\right ) x +b \right ) y^{\prime }-n \left (n +1\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.168 |
|
|
\[ {}\left (1+x \right ) x^{3} y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (10 x +4\right ) x y^{\prime }-4 \left (1+3 x \right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.52 |
|
|
\[ {}\left (x^{2}+1\right ) x^{3} y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.267 |
|
|
\[ {}x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.054 |
|
|
\[ {}x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.056 |
|
|
\[ {}x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
7.201 |
|
|
\[ {}\left (x -a \right )^{3} \left (x -b \right )^{3} y^{\prime \prime \prime }-c y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
78.088 |
|
|
\[ {}y^{\prime \prime \prime } \sin \left (x \right )+\left (2 \cos \left (x \right )+1\right ) y^{\prime \prime }-y^{\prime } \sin \left (x \right )-\cos \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _missing_y]] |
✗ |
N/A |
65.457 |
|
|
\[ {}\left (\sin \left (x \right )+x \right ) y^{\prime \prime \prime }+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }-3 y^{\prime } \sin \left (x \right )-y \cos \left (x \right )+\sin \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
N/A |
0.099 |
|
|
\[ {}y^{\prime \prime \prime } \sin \left (x \right )^{2}+3 y^{\prime \prime } \sin \left (x \right ) \cos \left (x \right )+\left (\cos \left (2 x \right )+4 \nu \left (\nu +1\right ) \sin \left (x \right )^{2}\right ) y^{\prime }+2 \nu \left (\nu +1\right ) y \sin \left (2 x \right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.105 |
|
|
\[ {}f^{\prime }\left (x \right ) y^{\prime \prime }+f \left (x \right ) y^{\prime \prime \prime }+g^{\prime }\left (x \right ) y^{\prime }+g \left (x \right ) y^{\prime \prime }+h^{\prime }\left (x \right ) y+h \left (x \right ) y^{\prime }+A \left (x \right ) \left (f \left (x \right ) y^{\prime \prime }+g \left (x \right ) y^{\prime }+h \left (x \right ) y\right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.118 |
|
|
\[ {}y^{\prime \prime \prime }+x y^{\prime }+n y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.131 |
|
|
\[ {}y^{\prime \prime \prime }-x y^{\prime }-n y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.129 |
|
|
\[ {}y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.184 |
|
|
\[ {}y^{\prime \prime \prime \prime }+\left (x^{2} a +b \lambda +c \right ) y^{\prime \prime }+\left (x^{2} a +\beta \lambda +\gamma \right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.211 |
|
|
\[ {}y^{\prime \prime \prime \prime }+a \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime \prime }+b \operatorname {WeierstrassPPrime}\left (x , \operatorname {g2} , \operatorname {g3}\right ) y^{\prime }+\left (c \left (6 \operatorname {WeierstrassP}\left (x , \operatorname {g2} , \operatorname {g3}\right )^{2}-\frac {\operatorname {g2}}{2}\right )+d \right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.103 |
|
|
\[ {}y^{\prime \prime \prime \prime }-\left (12 k^{2} \operatorname {JacobiSN}\left (z , x\right )^{2}+a \right ) y^{\prime \prime }+b y^{\prime }+\left (\alpha \operatorname {JacobiSN}\left (z , x\right )^{2}+\beta \right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.102 |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 a x y^{\prime \prime \prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a^{3} x^{3} y^{\prime }+a^{4} x^{4} y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.318 |
|
|
\[ {}y^{\prime \prime \prime \prime } x -\left (6 x^{2}+1\right ) y^{\prime \prime \prime }+12 x^{3} y^{\prime \prime }-\left (9 x^{2}-7\right ) x^{2} y^{\prime }+2 \left (x^{2}-3\right ) x^{3} y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.694 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }-2 \left (\nu ^{2} x^{2}+6\right ) y^{\prime \prime }+\nu ^{2} \left (\nu ^{2} x^{2}+4\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.376 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2} = 0 \] |
1 |
0 |
1 |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.102 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.244 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.26 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16} = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.291 |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime }-a^{4} x^{3} y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.276 |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (a \,x^{4}+n \left (n +1\right ) \left (n +3\right ) \left (n -2\right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.325 |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 y x^{4} = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.332 |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.319 |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.326 |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.347 |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.369 |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 b^{2} c^{2} x^{2 c}+6 \left (a -1\right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 a \left (a -1\right )-1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (-2 c +a \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.126 |
|
|
\[ {}x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (a -1\right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.128 |
|
|
\[ {}\nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16} = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.108 |
|
|
\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.6 |
|
|
\[ {}\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+{\mathrm e}^{x} y-\frac {1}{x^{5}} = 0 \] |
1 |
0 |
1 |
[[_high_order, _fully, _exact, _linear]] |
✗ |
N/A |
0.109 |
|
|
\[ {}y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.121 |
|
|
\[ {}y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f = 0 \] |
1 |
0 |
1 |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.112 |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (x a -b \right ) \left (y^{\prime \prime }-a^{2} y\right ) = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.108 |
|
|
\[ {}y^{\left (5\right )}-a x y-b = 0 \] |
1 |
0 |
0 |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.095 |
|
|
\[ {}y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.102 |
|
|
\[ {}x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.365 |
|
|
\[ {}x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y = 0 \] |
1 |
0 |
2 |
[[_high_order, _missing_x]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_high_order, _missing_y]] |
✗ |
N/A |
0.168 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }-a y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.237 |
|
|
\[ {}x^{10} y^{\left (5\right )}-a y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.056 |
|
|
\[ {}x^{\frac {5}{2}} y^{\left (5\right )}-a y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.096 |
|
|
\[ {}\left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y = 0 \] |
1 |
0 |
1 |
[[_high_order, _with_linear_symmetries]] |
✗ |
N/A |
55.836 |
|
|
\[ {}y^{\prime \prime }-6 y^{2}-x = 0 \] |
1 |
0 |
0 |
[[_Painleve, ‘1st‘]] |
✗ |
N/A |
0.071 |
|
|
\[ {}y^{\prime \prime }+a y^{2}+b x +c = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.081 |
|
|
\[ {}y^{\prime \prime }-2 y^{3}-x y+a = 0 \] |
1 |
0 |
0 |
[[_Painleve, ‘2nd‘]] |
✗ |
N/A |
0.077 |
|
|
\[ {}y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.083 |
|
|
\[ {}y^{\prime \prime }+d +b x y+c y+a y^{3} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.078 |
|
|
\[ {}y^{\prime \prime }+a \,x^{r} y^{2} = 0 \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.078 |
|
|
\[ {}y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{\frac {3}{2}}} = 0 \] |
1 |
0 |
2 |
[NONE] |
✗ |
N/A |
0.122 |
|
|
\[ {}y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.082 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.158 |
|
|
\[ {}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.322 |
|
|
\[ {}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.169 |
|
|
\[ {}y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{\frac {3}{2}}} \] |
1 |
0 |
3 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.198 |
|
|
\[ {}y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.122 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.082 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.118 |
|
|
\[ {}y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+y^{2} f \left (x \right )+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.089 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime }-y^{3}-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right )\right ) \left (3 y^{\prime }+y^{2}\right )+\left (a f \left (x \right )^{2}+3 f^{\prime }\left (x \right )+\frac {3 {f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}\right ) y+b f \left (x \right )^{3} = 0 \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
0.113 |
|
|
\[ {}y^{\prime \prime }+\left (y-\frac {3 f^{\prime }\left (x \right )}{2 f \left (x \right )}\right ) y^{\prime }-y^{3}-\frac {f^{\prime }\left (x \right ) y^{2}}{2 f \left (x \right )}+\frac {\left (f \left (x \right )+\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-f^{\prime \prime }\left (x \right )\right ) y}{2 f \left (x \right )} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.105 |
|
|
\[ {}y^{\prime \prime }+2 y y^{\prime }+f \left (x \right ) \left (y^{\prime }+y^{2}\right )-g \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.081 |
|
|
\[ {}y^{\prime \prime }+3 y y^{\prime }+y^{3}+f \left (x \right ) y-g \left (x \right ) = 0 \] |
1 |
0 |
1 |
[NONE] |
✗ |
N/A |
0.078 |
|
|
\[ {}y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_potential_symmetries]] |
✗ |
N/A |
0.079 |
|
|
\[ {}y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_potential_symmetries]] |
✗ |
N/A |
0.078 |
|
|
\[ {}y^{\prime \prime }+f \left (x , y\right ) y^{\prime }+g \left (x , y\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.085 |
|
|
\[ {}y^{\prime \prime }-\frac {D\left (f \right )\left (y\right ) {y^{\prime }}^{3}}{f \left (y\right )}+g \left (x \right ) y^{\prime }+h \left (x \right ) f \left (y\right ) = 0 \] |
0 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime }+\phi \left (y\right ) {y^{\prime }}^{2}+f \left (x \right ) y^{\prime }+g \left (x \right ) \Phi \left (y\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.119 |
|
|
\[ {}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (y\right ) y^{\prime }+h \left (y\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.134 |
|
|
\[ {}y^{\prime \prime }+\left (1+{y^{\prime }}^{2}\right ) \left (f \left (x , y\right ) y^{\prime }+g \left (x , y\right )\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.085 |
|
|
\[ {}y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{v} = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.083 |
|
|
\[ {}y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.083 |
|
|
\[ {}y^{\prime \prime }+\left (y^{\prime }-\frac {y}{x}\right )^{a} f \left (x , y\right ) = 0 \] |
0 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.122 |
|
|
\[ {}y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
2 |
0 |
4 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
N/A |
0.119 |
|
|
\[ {}y^{\prime \prime }-f \left (y^{\prime }, x a +b y\right ) = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.089 |
|
|
\[ {}y^{\prime \prime }-y f \left (x , \frac {y^{\prime }}{y}\right ) = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.08 |
|
|
\[ {}y^{\prime \prime }-x^{n -2} f \left (y x^{-n}, y^{\prime } x^{-n +1}\right ) = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.102 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.08 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0 \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.082 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.077 |
|
|
\[ {}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.079 |
|
|
\[ {}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.085 |
|
|
\[ {}x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.081 |
|
|
\[ {}x y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.083 |
|
|
\[ {}x^{2} y^{\prime \prime } = a \left (y^{n}-y\right ) \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.083 |
|
|
\[ {}x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.085 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (1+a \right ) x y^{\prime }-x^{k} f \left (x^{k} y, x y^{\prime }+k y\right ) = 0 \] |
0 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.105 |
|
|
\[ {}x^{2} y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b \,x^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.083 |
|
|
\[ {}x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.075 |
|
|
\[ {}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0 \] |
2 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.125 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.079 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+a y^{3}+2 y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.105 |
|
|
\[ {}x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.082 |
|
|
\[ {}x^{3} y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.082 |
|
|
\[ {}2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.086 |
|
|
\[ {}2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.101 |
|
|
\[ {}x^{4} y^{\prime \prime }+a^{2} y^{n} = 0 \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.082 |
|
|
\[ {}x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.08 |
|
|
\[ {}x^{4} y^{\prime \prime }-x^{2} \left (x +y^{\prime }\right ) y^{\prime }+4 y^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.081 |
|
|
\[ {}x^{4} y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{3} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.083 |
|
|
\[ {}y^{\prime \prime } \sqrt {x}-y^{\frac {3}{2}} = 0 \] |
1 |
0 |
2 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.084 |
|
|
\[ {}\left (x^{2} a +b x +c \right )^{\frac {3}{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {x^{2} a +b x +c}}\right ) = 0 \] |
1 |
0 |
3 |
[NONE] |
✗ |
N/A |
11.394 |
|
|
\[ {}x^{\frac {n}{n +1}} y^{\prime \prime }-y^{\frac {1+2 n}{n +1}} = 0 \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.118 |
|
|
\[ {}f \left (x \right )^{2} y^{\prime \prime }+f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }-h \left (y, f \left (x \right ) y^{\prime }\right ) = 0 \] |
0 |
0 |
1 |
[NONE] |
✗ |
N/A |
0.093 |
|
|
\[ {}y y^{\prime \prime }-x a = 0 \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.073 |
|
|
\[ {}y y^{\prime \prime }-x^{2} a = 0 \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.075 |
|
|
\[ {}y y^{\prime \prime }+y^{2}-x a -b = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.083 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.106 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{\prime }+f \left (x \right ) y^{3}+y^{2} \left (\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.105 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.089 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-f^{\prime \prime }\left (x \right ) y+f \left (x \right ) y^{3}-y^{4} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.099 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
1.138 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.089 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2}+\left (g \left (x \right )+y^{2} f \left (x \right )\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.101 |
|
|
\[ {}y y^{\prime \prime }+a {y^{\prime }}^{2}+f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.089 |
|
|
\[ {}y y^{\prime \prime }-\frac {\left (a -1\right ) {y^{\prime }}^{2}}{a}-f \left (x \right ) y^{2} y^{\prime }+\frac {a f \left (x \right )^{2} y^{4}}{\left (2+a \right )^{2}}-\frac {a f^{\prime }\left (x \right ) y^{3}}{2+a} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.118 |
|
|
\[ {}y^{\prime \prime } \left (x -y\right )+2 y^{\prime } \left (y^{\prime }+1\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
N/A |
0.082 |
|
|
\[ {}y^{\prime \prime } \left (x -y\right )-\left (y^{\prime }+1\right ) \left (1+{y^{\prime }}^{2}\right ) = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
N/A |
0.081 |
|
|
\[ {}y^{\prime \prime } \left (x -y\right )-h \left (y^{\prime }\right ) = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
N/A |
0.155 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+y^{2} f \left (x \right )+a = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.083 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 \left (2 y+x \right ) y^{2} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.085 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.086 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.086 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0 \] |
1 |
0 |
0 |
[[_Painleve, ‘4th‘]] |
✗ |
N/A |
0.091 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+3 f \left (x \right ) y y^{\prime }+2 \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y^{2}-8 y^{3} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.099 |
|
|
\[ {}2 y y^{\prime \prime }-{y^{\prime }}^{2}+4 y^{2} y^{\prime }+1+y^{2} f \left (x \right )+y^{4} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.09 |
|
|
\[ {}2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+y^{2} f \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.085 |
|
|
\[ {}3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-x^{2} a -b x -c = 0 \] |
1 |
0 |
2 |
[NONE] |
✗ |
N/A |
0.089 |
|
|
\[ {}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+\left (6 y^{2}-\frac {2 f^{\prime }\left (x \right ) y}{f \left (x \right )}\right ) y^{\prime }+y^{4}-2 y^{2} y^{\prime }+g \left (x \right ) y^{2}+f \left (x \right ) y = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.11 |
|
|
\[ {}a y y^{\prime \prime }-\left (a -1\right ) {y^{\prime }}^{2}+\left (2+a \right ) f \left (x \right ) y^{2} y^{\prime }+f \left (x \right )^{2} y^{4}+a f^{\prime }\left (x \right ) y^{3} = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.106 |
|
|
\[ {}x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0 \] |
1 |
0 |
0 |
[[_Painleve, ‘3rd‘]] |
✗ |
N/A |
0.093 |
|
|
\[ {}x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.094 |
|
|
\[ {}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (y+1\right ) y^{\prime } = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.087 |
|
|
\[ {}x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y y^{\prime } = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.247 |
|
|
\[ {}x^{2} \left (y-1\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (y-1\right ) y^{\prime }-2 y \left (y-1\right )^{2} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.144 |
|
|
\[ {}x^{2} \left (x +y\right ) y^{\prime \prime }-\left (-y+x y^{\prime }\right )^{2} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.096 |
|
|
\[ {}x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.096 |
|
|
\[ {}2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.093 |
|
|
\[ {}a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.102 |
|
|
\[ {}x \left (1+x \right )^{2} y y^{\prime \prime }-x \left (1+x \right )^{2} {y^{\prime }}^{2}+2 \left (1+x \right )^{2} y y^{\prime }-a \left (2+x \right ) y^{2} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.115 |
|
|
\[ {}8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.131 |
|
|
\[ {}\operatorname {f0} \left (x \right ) y y^{\prime \prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f3} \left (x \right ) y^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.115 |
|
|
\[ {}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+x a = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.094 |
|
|
\[ {}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-x a -b = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.086 |
|
|
\[ {}\left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right ) = 0 \] |
1 |
0 |
3 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
N/A |
0.105 |
|
|
|
||||||||
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (-y+x y^{\prime }\right ) = 0 \] |
1 |
0 |
3 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
N/A |
0.1 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (-y+x y^{\prime }\right ) = 0 \] |
1 |
0 |
4 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
N/A |
0.099 |
|
|
\[ {}2 y \left (1-y\right ) y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+y \left (1-y\right ) y^{\prime } f \left (x \right ) = 0 \] |
1 |
0 |
1 |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.115 |
|
|
\[ {}2 y \left (1-y\right ) y^{\prime \prime }-\left (-3 y+1\right ) {y^{\prime }}^{2}+h \left (y\right ) = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.141 |
|
|
\[ {}2 y \left (y-1\right ) y^{\prime \prime }-\left (3 y-1\right ) {y^{\prime }}^{2}+4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+4 y^{2} \left (y-1\right ) \left (g \left (x \right )^{2}-f \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.133 |
|
|
\[ {}-2 y \left (1-y\right ) y^{\prime \prime }+\left (-3 y+1\right ) {y^{\prime }}^{2}-4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+\left (1-y\right )^{3} \left (\operatorname {f0} \left (x \right )^{2} y^{2}-\operatorname {f1} \left (x \right )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \left (x \right )^{2}-g \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.145 |
|
|
\[ {}3 y \left (1-y\right ) y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.151 |
|
|
\[ {}\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.128 |
|
|
\[ {}a y \left (y-1\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.135 |
|
|
\[ {}x y^{2} y^{\prime \prime }-a = 0 \] |
1 |
0 |
4 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.095 |
|
|
\[ {}\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime } = 0 \] |
1 |
0 |
3 |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.112 |
|
|
\[ {}2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (y+1\right ) = 0 \] |
1 |
0 |
0 |
[[_Painleve, ‘5th‘]] |
✗ |
N/A |
0.124 |
|
|
\[ {}x^{3} y^{2} y^{\prime \prime }+\left (x +y\right ) \left (-y+x y^{\prime }\right )^{3} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.116 |
|
|
\[ {}2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.112 |
|
|
\[ {}2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-x^{2} a -b x -c = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.108 |
|
|
\[ {}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }+x \left (1-x \right ) \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}+2 y \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }-y^{2} \left (1-y\right )^{2}-f \left (y \left (y-1\right ) \left (y-x \right )\right )^{\frac {3}{2}} = 0 \] |
1 |
0 |
0 |
unknown |
✗ |
N/A |
0.214 |
|
|
\[ {}2 x^{2} y \left (1-x \right )^{2} \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }-x^{2} \left (1-x \right )^{2} \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }+b x \left (1-y\right )^{2} \left (x -y\right )^{2}-c \left (1-x \right ) y^{2} \left (x -y\right )^{2}-d x y^{2} \left (1-x \right ) \left (1-y\right )^{2}+a y^{2} \left (x -y\right )^{2} \left (1-y\right )^{2} = 0 \] |
1 |
0 |
0 |
[[_Painleve, ‘6th‘]] |
✗ |
N/A |
0.208 |
|
|
\[ {}\left (c +2 b x +x^{2} a +y^{2}\right )^{2} y^{\prime \prime }+d y = 0 \] |
1 |
0 |
2 |
[NONE] |
✗ |
N/A |
0.107 |
|
|
\[ {}\sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} = 0 \] |
2 |
0 |
3 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.17 |
|
|
\[ {}h \left (y\right ) y^{\prime \prime }+a D\left (h \right )\left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0 \] |
0 |
0 |
2 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.0 |
|
|
\[ {}h \left (y\right ) y^{\prime \prime }-D\left (h \right )\left (y\right ) {y^{\prime }}^{2}-h \left (y\right )^{2} j \left (x , \frac {y^{\prime }}{h \left (y\right )}\right ) = 0 \] |
0 |
0 |
1 |
[NONE] |
✗ |
N/A |
0.0 |
|
|
\[ {}\left (-y+x y^{\prime }\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.101 |
|
|
\[ {}\left (-y+x y^{\prime }\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0 \] |
1 |
0 |
3 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.096 |
|
|
\[ {}a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.101 |
|
|
\[ {}\left (\operatorname {f1} y^{\prime }+\operatorname {f2} y\right ) y^{\prime \prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f4} \left (x \right ) y y^{\prime }+\operatorname {f5} \left (x \right ) y^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.111 |
|
|
\[ {}\left ({y^{\prime }}^{2}+a \left (-y+x y^{\prime }\right )\right ) y^{\prime \prime }-b = 0 \] |
1 |
0 |
4 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.1 |
|
|
\[ {}h \left (y^{\prime }\right ) y^{\prime \prime }+j \left (y\right ) y^{\prime }+f = 0 \] |
0 |
0 |
1 |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
N/A |
0.227 |
|
|
\[ {}2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x y^{\prime \prime } \left (x +4 y^{\prime }\right )+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0 \] |
2 |
0 |
2 |
[NONE] |
✗ |
N/A |
0.197 |
|
|
\[ {}3 x^{2} {y^{\prime \prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0 \] |
2 |
0 |
3 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.187 |
|
|
\[ {}x^{2} \left (2-9 x \right ) {y^{\prime \prime }}^{2}-6 x \left (1-6 x \right ) y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2} = 0 \] |
2 |
0 |
4 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.224 |
|
|
\[ {}F_{1,1}\left (x \right ) {y^{\prime }}^{2}+\left (\left (F_{2,1}\left (x \right )+F_{1,2}\left (x \right )\right ) y^{\prime \prime }+y \left (F_{1,0}\left (x \right )+F_{0,1}\left (x \right )\right )\right ) y^{\prime }+F_{2,2}\left (x \right ) {y^{\prime \prime }}^{2}+y \left (F_{2,0}\left (x \right )+F_{0,2}\left (x \right )\right ) y^{\prime \prime }+F_{0,0}\left (x \right ) y^{2} = 0 \] |
2 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.437 |
|
|
\[ {}y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0 \] |
2 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.235 |
|
|
\[ {}\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (-y+x y^{\prime }\right )^{3} = 0 \] |
2 |
0 |
3 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.202 |
|
|
\[ {}\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3} = 0 \] |
4 |
0 |
0 |
unknown |
✗ |
N/A |
0.447 |
|
|
\[ {}y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right ) = 0 \] |
1 |
0 |
2 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime }-y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime }+a y y^{\prime \prime } = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }+\left (2 x y-1\right ) y^{\prime }+y^{2}-f \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+x \left (y-1\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime } = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y y^{\prime \prime \prime }-y^{\prime } y^{\prime \prime }+y^{3} y^{\prime } = 0 \] |
1 |
0 |
3 |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}4 y^{2} y^{\prime \prime \prime }-18 y y^{\prime } y^{\prime \prime }+15 {y^{\prime }}^{3} = 0 \] |
1 |
0 |
3 |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}9 y^{2} y^{\prime \prime \prime }-45 y y^{\prime } y^{\prime \prime }+40 {y^{\prime }}^{3} = 0 \] |
1 |
0 |
3 |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}2 y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime }}^{2} = 0 \] |
1 |
0 |
2 |
[[_3rd_order, _missing_x]] |
✗ |
N/A |
0.0 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {y^{\prime \prime }}^{2} = 0 \] |
1 |
0 |
4 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✗ |
N/A |
0.0 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-\left (3 y^{\prime }+a \right ) {y^{\prime \prime }}^{2} = 0 \] |
1 |
0 |
4 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {b^{2} {y^{\prime \prime }}^{2}+1} = 0 \] |
1 |
0 |
4 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime } = 0 \] |
1 |
0 |
2 |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime } \left (f^{\prime \prime \prime }\left (x \right ) y^{\prime }+3 f^{\prime \prime }\left (x \right ) y^{\prime \prime }+3 f^{\prime }\left (x \right ) y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime \prime \prime }\right )-y^{\prime \prime } f y^{\prime \prime \prime }+{y^{\prime }}^{3} \left (f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right ) y^{\prime \prime }\right )+2 q \left (x \right ) {y^{\prime }}^{2} \sin \left (y\right )+\left (q \left (x \right ) y^{\prime \prime }-q^{\prime }\left (x \right ) y^{\prime }\right ) \cos \left (y\right ) = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.0 |
|
|
\[ {}3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \] |
1 |
0 |
2 |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✗ |
N/A |
0.0 |
|
|
\[ {}9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime } = 0 \] |
1 |
0 |
2 |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime }-f \left (y\right ) = 0 \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
N/A |
0.19 |
|
|
\[ {}y^{\prime \prime \prime } = f \left (y\right ) \] |
1 |
0 |
1 |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )=f \left (t \right ) \\ x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )=g \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.94 |
|
|
\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )=0 \\ x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.934 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+x \left (t \right )=2 t \\ x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )-9 x \left (t \right )+3 y \left (t \right )=\sin \left (2 t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.918 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right )=0 \\ x^{\prime \prime }\left (t \right )-2 y^{\prime }\left (t \right )=2 t -\cos \left (2 t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.787 |
|
|
\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )-t y^{\prime }\left (t \right )-2 y \left (t \right )=0 \\ t x^{\prime \prime }\left (t \right )+2 x^{\prime }\left (t \right )+x \left (t \right ) t =0 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.918 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+a y \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )-a^{2} y \left (t \right )=0 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.907 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=a x \left (t \right )+b y \left (t \right ) \\ y^{\prime \prime }\left (t \right )=c x \left (t \right )+d y \left (t \right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.929 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1} \\ y^{\prime \prime }\left (t \right )=a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.937 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+x \left (t \right )+y \left (t \right )=-5 \\ y^{\prime \prime }\left (t \right )-4 x \left (t \right )-3 y \left (t \right )=-3 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.918 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x \left (t \right )+\frac {3 c^{2} y \left (t \right ) \sin \left (2 a t b \right )}{2} \\ y^{\prime \prime }\left (t \right )=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y \left (t \right )+\frac {3 c^{2} x \left (t \right ) \sin \left (2 a t b \right )}{2} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
1.841 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+6 x \left (t \right )+7 y \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right )=2 t \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.931 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-a y^{\prime }\left (t \right )+b x \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )+a x^{\prime }\left (t \right )+b y \left (t \right )=0 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.925 |
|
|
\[ {}\left [\begin {array}{c} a_{1} x^{\prime \prime }\left (t \right )+b_{1} x^{\prime }\left (t \right )+c_{1} x \left (t \right )-A y^{\prime }\left (t \right )=B \,{\mathrm e}^{i \omega t} \\ a_{2} y^{\prime \prime }\left (t \right )+b_{2} y^{\prime }\left (t \right )+c_{2} y \left (t \right )+A x^{\prime }\left (t \right )=0 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.934 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+a \left (x^{\prime }\left (t \right )-y^{\prime }\left (t \right )\right )+b_{1} x \left (t \right )=c_{1} {\mathrm e}^{i \omega t} \\ y^{\prime \prime }\left (t \right )+a \left (y^{\prime }\left (t \right )-x^{\prime }\left (t \right )\right )+b_{2} y \left (t \right )=c_{2} {\mathrm e}^{i \omega t} \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.958 |
|
|
\[ {}\left [\begin {array}{c} \operatorname {a11} x^{\prime \prime }\left (t \right )+\operatorname {b11} x^{\prime }\left (t \right )+\operatorname {c11} x \left (t \right )+\operatorname {a12} y^{\prime \prime }\left (t \right )+\operatorname {b12} y^{\prime }\left (t \right )+\operatorname {c12} y \left (t \right )=0 \\ \operatorname {a21} x^{\prime \prime }\left (t \right )+\operatorname {b21} x^{\prime }\left (t \right )+\operatorname {c21} x \left (t \right )+\operatorname {a22} y^{\prime \prime }\left (t \right )+\operatorname {b22} y^{\prime }\left (t \right )+\operatorname {c22} y \left (t \right )=0 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.945 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+y \left (t \right )=0 \\ y^{\prime \prime \prime }\left (t \right )-y^{\prime \prime }\left (t \right )+2 x^{\prime }\left (t \right )-x \left (t \right )=t \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.928 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )=\sinh \left (2 t \right ) \\ 2 x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )=2 t \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.92 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=0 \\ x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )-x \left (t \right )=0 \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.917 |
|
|
\[ {}\left [\begin {array}{c} x \left (t \right )=t x^{\prime }\left (t \right )+f \left (x^{\prime }\left (t \right ), y^{\prime }\left (t \right )\right ) \\ y \left (t \right )=t y^{\prime }\left (t \right )+g \left (x^{\prime }\left (t \right ), y^{\prime }\left (t \right )\right ) \end {array}\right ] \] |
1 |
0 |
2 |
system of linear ODEs |
✗ |
N/A |
0.899 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=a \,{\mathrm e}^{2 x \left (t \right )}-{\mathrm e}^{-x \left (t \right )}+{\mathrm e}^{-2 x \left (t \right )} \cos \left (y \left (t \right )\right )^{2} \\ y^{\prime \prime }\left (t \right )={\mathrm e}^{-2 x \left (t \right )} \sin \left (y \left (t \right )\right ) \cos \left (y \left (t \right )\right )-\frac {\sin \left (y \left (t \right )\right )}{\cos \left (y \left (t \right )\right )^{3}} \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
1.807 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=\frac {k x \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{\frac {3}{2}}} \\ y^{\prime \prime }\left (t \right )=\frac {k y \left (t \right )}{\left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )^{\frac {3}{2}}} \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
✗ |
N/A |
1.81 |
|
|
\[ {}y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )} \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
0.245 |
|
|
\[ {}y y^{\prime }-y = -\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.157 |
|
|
\[ {}y y^{\prime }-y = 2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right ) \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.533 |
|
|
\[ {}y y^{\prime }-y = A x +\frac {B}{x}-\frac {B^{2}}{x^{3}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.716 |
|
|
\[ {}y y^{\prime }-y = A \,x^{k -1}-k B \,x^{k}+k \,B^{2} x^{2 k -1} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.948 |
|
|
\[ {}y y^{\prime }-y = \frac {A}{x}-\frac {A^{2}}{x^{3}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.587 |
|
|
\[ {}y y^{\prime }-y = A +B \,{\mathrm e}^{-\frac {2 x}{A}} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.711 |
|
|
\[ {}y y^{\prime }-y = A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.691 |
|
|
\[ {}y y^{\prime }-y = -\frac {2 \left (1+m \right )}{\left (3+m \right )^{2}}+A \,x^{m} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.085 |
|
|
\[ {}y y^{\prime }-y = -\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.686 |
|
|
\[ {}y y^{\prime }-y = \frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (3+m \right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (3+m \right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
4.787 |
|
|
\[ {}y y^{\prime }-y = \frac {\left (1+2 m \right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.888 |
|
|
\[ {}y y^{\prime }-y = \frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.655 |
|
|
\[ {}y y^{\prime }-y = -\frac {3 x}{16}+\frac {5 A}{x^{\frac {1}{3}}}-\frac {12 A^{2}}{x^{\frac {5}{3}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.621 |
|
|
\[ {}y y^{\prime }-y = \frac {A}{x} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.483 |
|
|
\[ {}y y^{\prime }-y = -\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
4.425 |
|
|
\[ {}y y^{\prime }-y = \frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.202 |
|
|
\[ {}y y^{\prime }-y = 2 x +\frac {A}{x^{2}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.499 |
|
|
\[ {}y y^{\prime }-y = -\frac {6 X}{25}+\frac {2 A \left (2 \sqrt {x}+19 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{25} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.227 |
|
|
\[ {}y y^{\prime }-y = \frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.723 |
|
|
\[ {}y y^{\prime }-y = -\frac {4 x}{25}+\frac {A}{\sqrt {x}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.241 |
|
|
\[ {}y y^{\prime }-y = -\frac {9 x}{100}+\frac {A}{x^{\frac {5}{3}}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.227 |
|
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.263 |
|
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.296 |
|
|
\[ {}y y^{\prime }-y = -\frac {2 x}{9}+\frac {A}{\sqrt {x}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.135 |
|
|
\[ {}y y^{\prime }-y = -\frac {5 x}{36}+\frac {A}{x^{\frac {7}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.399 |
|
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.559 |
|
|
\[ {}y y^{\prime }-y = -\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.225 |
|
|
\[ {}y y^{\prime }-y = -\frac {3 x}{16}+\frac {A}{x^{\frac {5}{3}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.228 |
|
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.65 |
|
|
\[ {}y y^{\prime }-y = \frac {A}{\sqrt {x}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.033 |
|
|
\[ {}y y^{\prime }-y = \frac {A}{x^{2}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.48 |
|
|
\[ {}y y^{\prime }-y = A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.729 |
|
|
\[ {}y y^{\prime }-y = A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (3+2 n \right ) A^{2}}{\sqrt {x}}\right ) \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.452 |
|
|
\[ {}y y^{\prime }-y = A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.726 |
|
|
\[ {}y y^{\prime }-y = 2 A^{2}-A \sqrt {x} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.938 |
|
|
\[ {}y y^{\prime }-y = -\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.223 |
|
|
\[ {}y y^{\prime }-y = -\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.659 |
|
|
\[ {}y y^{\prime }-y = -\frac {3 x}{16}+\frac {3 A}{x^{\frac {1}{3}}}-\frac {12 A^{2}}{x^{\frac {5}{3}}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.962 |
|
|
\[ {}y y^{\prime }-y = \frac {3 x}{8}+\frac {3 \sqrt {b^{2}+x^{2}}}{8}+\frac {3 b^{2}}{16 \sqrt {b^{2}+x^{2}}} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.742 |
|
|
\[ {}y y^{\prime }-y = \frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.853 |
|
|
\[ {}y y^{\prime }-y = -\frac {3 x}{32}-\frac {3 \sqrt {a^{2}+x^{2}}}{32}+\frac {15 a^{2}}{64 \sqrt {a^{2}+x^{2}}} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.006 |
|
|
\[ {}y y^{\prime }-y = A \,x^{2}-\frac {9}{625 A} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.58 |
|
|
\[ {}y y^{\prime }-y = -\frac {6}{25} x -A \,x^{2} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.482 |
|
|
\[ {}y y^{\prime }-y = \frac {6}{25} x -A \,x^{2} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.459 |
|
|
\[ {}y y^{\prime }-y = 12 x +\frac {A}{x^{\frac {5}{2}}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.59 |
|
|
\[ {}y y^{\prime }-y = \frac {63 x}{4}+\frac {A}{x^{\frac {5}{3}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.24 |
|
|
\[ {}y y^{\prime }-y = 2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.744 |
|
|
\[ {}y y^{\prime }-y = 2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.258 |
|
|
\[ {}y y^{\prime }-y = -\frac {28 x}{121}+\frac {2 A \left (5 \sqrt {x}+106 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{121} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.323 |
|
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.257 |
|
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+A \sqrt {x} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
2.723 |
|
|
\[ {}y y^{\prime }-y = 6 x +\frac {A}{x^{4}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.524 |
|
|
\[ {}y y^{\prime }-y = 20 x +\frac {A}{\sqrt {x}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.193 |
|
|
\[ {}y y^{\prime }-y = \frac {15 x}{4}+\frac {A}{x^{7}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.547 |
|
|
\[ {}y y^{\prime }-y = -\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.206 |
|
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.283 |
|
|
\[ {}y y^{\prime }-y = -\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.3 |
|
|
\[ {}y y^{\prime }-y = \frac {15 x}{4}+\frac {6 A}{x^{\frac {1}{3}}}-\frac {3 A^{2}}{x^{\frac {5}{3}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.967 |
|
|
\[ {}y y^{\prime }-y = -\frac {3 x}{16}+\frac {A}{x^{\frac {1}{3}}}+\frac {B}{x^{\frac {5}{3}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
5.272 |
|
|
\[ {}y y^{\prime }-y = -\frac {5 x}{36}+\frac {A}{x^{\frac {3}{5}}}-\frac {B}{x^{\frac {7}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.936 |
|
|
\[ {}y y^{\prime }-y = \frac {k}{\sqrt {A \,x^{2}+B x +c}} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.929 |
|
|
\[ {}y y^{\prime }-y = -\frac {12 x}{49}+3 A \left (\frac {1}{49}+B \right ) \sqrt {x}+3 A^{2} \left (\frac {4}{49}-\frac {5 B}{2}\right )+\frac {15 A^{3} \left (\frac {1}{49}-\frac {5 B}{4}\right )}{4 \sqrt {x}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.879 |
|
|
\[ {}y y^{\prime }-y = -\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{\frac {1}{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{\frac {1}{3}}}-\frac {A \,B^{3}}{x^{\frac {2}{3}}}\right )}{75} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.215 |
|
|
\[ {}y y^{\prime }-y = \frac {3 x}{4}-\frac {3 A \,x^{\frac {1}{3}}}{2}+\frac {3 A^{2}}{4 x^{\frac {1}{3}}}-\frac {27 A^{4}}{625 x^{\frac {5}{3}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.771 |
|
|
\[ {}y y^{\prime }-y = -\frac {6 x}{25}+\frac {7 A \,x^{\frac {1}{3}}}{5}+\frac {31 A^{2}}{3 x^{\frac {1}{3}}}-\frac {100 A^{4}}{3 x^{\frac {5}{3}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.717 |
|
|
\[ {}y y^{\prime }-y = -\frac {10 x}{49}+\frac {13 A^{2}}{5 x^{\frac {1}{5}}}-\frac {7 A^{3}}{20 x^{\frac {4}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.009 |
|
|
\[ {}y y^{\prime }-y = -\frac {33 x}{169}+\frac {286 A^{2}}{3 x^{\frac {5}{11}}}-\frac {770 A^{3}}{9 x^{\frac {13}{11}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.461 |
|
|
\[ {}y y^{\prime }-y = -\frac {21 x}{100}+\frac {7 A^{2} \left (\frac {123}{x^{\frac {1}{7}}}+\frac {280 A}{x^{\frac {5}{7}}}-\frac {400 A^{2}}{x^{\frac {9}{7}}}\right )}{9} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.716 |
|
|
\[ {}y y^{\prime }-y = x a +b \,x^{m} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.724 |
|
|
\[ {}y y^{\prime }-y = -\frac {\left (1+m \right ) x}{\left (m +2\right )^{2}}+A \,x^{1+2 m}+B \,x^{3 m +1} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.661 |
|
|
\[ {}y y^{\prime }-y = a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.615 |
|
|
\[ {}y y^{\prime }-y = a^{2} \lambda \,{\mathrm e}^{2 \lambda x}+a \lambda x \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\lambda x} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.072 |
|
|
\[ {}y y^{\prime }-y = 2 a^{2} \lambda \sin \left (2 \lambda x \right )+2 a \sin \left (\lambda x \right ) \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.978 |
|
|
\[ {}y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.249 |
|
|
\[ {}y y^{\prime } = \left (x a +b \right ) y+1 \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.652 |
|
|
\[ {}y y^{\prime } = \frac {y}{\left (x a +b \right )^{2}}+1 \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.056 |
|
|
\[ {}y y^{\prime } = \left (a -\frac {1}{a x}\right ) y+1 \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.592 |
|
|
\[ {}y y^{\prime } = \frac {3 y}{\sqrt {a \,x^{\frac {3}{2}}+8 x}}+1 \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.617 |
|
|
\[ {}y y^{\prime } = \left (\frac {a}{x^{\frac {2}{3}}}-\frac {2}{3 a \,x^{\frac {1}{3}}}\right ) y+1 \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.618 |
|
|
\[ {}y y^{\prime } = a \,{\mathrm e}^{\lambda x} y+1 \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.558 |
|
|
\[ {}y y^{\prime } = \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{-\lambda x}\right ) y+1 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.842 |
|
|
\[ {}y y^{\prime } = a y \cosh \left (x \right )+1 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.768 |
|
|
\[ {}y y^{\prime } = a y \sinh \left (x \right )+1 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.849 |
|
|
\[ {}y y^{\prime } = a \cos \left (\lambda x \right ) y+1 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.878 |
|
|
\[ {}y y^{\prime } = a \sin \left (\lambda x \right ) y+1 \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.937 |
|
|
\[ {}y y^{\prime } = \left (x a +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.943 |
|
|
\[ {}2 y y^{\prime } = \left (7 x a +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.571 |
|
|
\[ {}y y^{\prime } = \left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) x a \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.776 |
|
|
\[ {}y y^{\prime }+x \left (x^{2} a +b \right ) y+x = 0 \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.535 |
|
|
\[ {}y y^{\prime }+a \left (1-\frac {1}{x}\right ) y = a^{2} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.596 |
|
|
\[ {}y y^{\prime }-a \left (1-\frac {b}{x}\right ) y = a^{2} b \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.626 |
|
|
\[ {}y y^{\prime } = x^{n -1} \left (\left (1+2 n \right ) x +a n \right ) y-n \,x^{2 n} \left (x +a \right ) \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.243 |
|
|
\[ {}y y^{\prime } = a \left (-n b +x \right ) x^{n -1} y+c \left (x^{2}-\left (1+2 n \right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.938 |
|
|
\[ {}y y^{\prime } = \left (a \left (2 n +k \right ) x^{k}+b \right ) x^{n -1} y+\left (-a^{2} n \,x^{2 k}-a b \,x^{k}+c \right ) x^{2 n -1} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.699 |
|
|
\[ {}y y^{\prime } = \left (a \left (2 n +k \right ) x^{2 k}+b \left (2 m -k \right )\right ) x^{m -k -1} y-\frac {a^{2} m \,x^{4 k}+c \,x^{2 k}+b^{2} m}{x} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.989 |
|
|
\[ {}y y^{\prime } = \frac {\left (\left (m +2 L -3\right ) x +n -2 L +3\right ) y}{x}+\left (\left (m -L -1\right ) x^{2}+\left (n -m -2 L +3\right ) x -n +L -2\right ) x^{1-2 L} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.241 |
|
|
\[ {}y y^{\prime } = \left (a \left (1+2 n \right ) x^{2}+c x +b \left (2 n -1\right )\right ) x^{n -2} y-\left (n \,a^{2} x^{4}+a c \,x^{3}+b^{2} n +c b x +d \,x^{2}\right ) x^{-3+2 n} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
2.134 |
|
|
\[ {}y y^{\prime } = \left (a \left (n -1\right ) x +b \left (2 \lambda +n \right )\right ) x^{\lambda -1} \left (x a +b \right )^{-\lambda -2} y-\left (a x n +b \left (\lambda +n \right )\right ) x^{2 \lambda -1} \left (x a +b \right )^{-2 \lambda -3} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.847 |
|
|
\[ {}y y^{\prime }-\frac {a \left (\left (m -1\right ) x +1\right ) y}{x} = \frac {a^{2} \left (m x +1\right ) \left (-1+x \right )}{x} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.837 |
|
|
\[ {}y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y = \frac {a^{2} b}{\sqrt {x}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.307 |
|
|
\[ {}y y^{\prime } = \frac {3 y}{\left (x a +b \right )^{\frac {1}{3}} x^{\frac {5}{3}}}+\frac {3}{\left (x a +b \right )^{\frac {2}{3}} x^{\frac {7}{3}}} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.938 |
|
|
\[ {}3 y y^{\prime } = \frac {\left (-7 \lambda s \left (3 s +4 \lambda \right ) x +6 s -2 \lambda \right ) y}{x^{\frac {1}{3}}}+\frac {6 \lambda s x -6}{x^{\frac {2}{3}}}+2 \left (\lambda s \left (3 s +4 \lambda \right ) x +5 \lambda \right ) \left (-\lambda s \left (3 s +4 \lambda \right ) x +3 s +4 \lambda \right ) x^{\frac {1}{3}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.431 |
|
|
\[ {}y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x} = -\frac {a^{2} \left (-1+x \right ) \left (4 x -1\right )}{2 x} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.909 |
|
|
\[ {}y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2} = \frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.853 |
|
|
\[ {}y y^{\prime }+\frac {a \left (13 x -20\right ) y}{14 x^{\frac {9}{7}}} = -\frac {3 a^{2} \left (-1+x \right ) \left (x -8\right )}{14 x^{\frac {11}{17}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
30.817 |
|
|
\[ {}y y^{\prime }+\frac {5 a \left (23 x -16\right ) y}{56 x^{\frac {9}{7}}} = -\frac {3 a^{2} \left (-1+x \right ) \left (25 x -32\right )}{56 x^{\frac {11}{17}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
8.818 |
|
|
\[ {}y y^{\prime }+\frac {a \left (19 x +85\right ) y}{26 x^{\frac {18}{13}}} = -\frac {3 a^{2} \left (-1+x \right ) \left (x +25\right )}{26 x^{\frac {23}{13}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.283 |
|
|
\[ {}y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{\frac {7}{5}}} = -\frac {4 a^{2} \left (-1+x \right ) \left (x -6\right )}{15 x^{\frac {9}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.372 |
|
|
\[ {}y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}} = a^{2} \left (-x^{2}+1\right ) \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.818 |
|
|
\[ {}y y^{\prime }+\frac {3 a \left (19 x -14\right ) x^{\frac {7}{5}} y}{35} = -\frac {4 a^{2} \left (-1+x \right ) \left (9 x -14\right ) x^{\frac {9}{5}}}{35} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.545 |
|
|
\[ {}y y^{\prime }+\frac {3 a \left (3 x +7\right ) y}{10 x^{\frac {13}{10}}} = -\frac {a^{2} \left (-1+x \right ) \left (x +9\right )}{5 x^{\frac {8}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
36.145 |
|
|
\[ {}y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{\frac {7}{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -16\right )}{10 x^{\frac {9}{5}}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.353 |
|
|
\[ {}y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{\frac {7}{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (27 x -32\right )}{20 x^{\frac {9}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.264 |
|
|
\[ {}y y^{\prime }+\frac {3 a \left (3 x +11\right ) y}{14 x^{\frac {10}{7}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -27\right )}{14 x^{\frac {13}{7}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.253 |
|
|
\[ {}y y^{\prime }-\frac {a \left (1+x \right ) y}{2 x^{\frac {7}{4}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +5\right )}{4 x^{\frac {5}{2}}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
8.809 |
|
|
\[ {}y y^{\prime }-\frac {a \left (1+x \right ) y}{2 x^{\frac {7}{4}}} = \frac {a^{2} \left (-1+x \right ) \left (x +5\right )}{4 x^{\frac {5}{2}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
8.52 |
|
|
\[ {}y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{\frac {8}{7}}} = -\frac {a^{2} \left (-1+x \right ) \left (16 x +5\right )}{14 x^{\frac {9}{7}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.339 |
|
|
\[ {}y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{\frac {2}{3}}} = -\frac {a^{2} \left (-1+x \right ) \left (5 x -1\right )}{6 x^{\frac {1}{3}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
5.437 |
|
|
\[ {}y y^{\prime }-\frac {a \left (8 x -1\right ) y}{28 x^{\frac {8}{7}}} = \frac {a^{2} \left (-1+x \right ) \left (32 x +3\right )}{28 x^{\frac {9}{7}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.278 |
|
|
\[ {}y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}} = \frac {a^{2} \left (-1+x \right ) \left (3 x -1\right )}{x^{7}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.916 |
|
|
\[ {}y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}} = \frac {a^{2} \left (-1+x \right ) \left (8 x -5\right )}{5 x^{7}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.917 |
|
|
\[ {}y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{\frac {9}{7}}} = -\frac {a^{2} \left (-1+x \right ) \left (9 x -1\right )}{42 x^{\frac {11}{7}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.349 |
|
|
\[ {}y y^{\prime }+\frac {a \left (-2+x \right ) y}{x} = \frac {2 a^{2} \left (-1+x \right )}{x} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.649 |
|
|
\[ {}y y^{\prime }+\frac {a \left (-2+3 x \right ) y}{x} = -\frac {2 a^{2} \left (-1+x \right )^{2}}{x} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.349 |
|
|
\[ {}y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x} = \frac {a^{2} b}{x} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.694 |
|
|
|
||||||||
|
\[ {}y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{\frac {5}{2}}} = \frac {a^{2} \left (-1+x \right ) \left (2+x \right )}{4 x^{4}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.134 |
|
|
\[ {}y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{\frac {6}{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (9 x -4\right )}{30 x^{\frac {7}{5}}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.35 |
|
|
\[ {}y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{\frac {5}{2}}} = -\frac {a^{2} \left (-1+x \right ) \left (3 x -4\right )}{8 x^{4}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.372 |
|
|
\[ {}y y^{\prime }+\frac {a \left (17 x +18\right ) y}{30 x^{\frac {22}{15}}} = -\frac {a^{2} \left (-1+x \right ) \left (x +4\right )}{30 x^{\frac {29}{15}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
22.907 |
|
|
\[ {}y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{\frac {5}{2}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -13\right )}{26 x^{4}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.505 |
|
|
\[ {}y y^{\prime }+\frac {a \left (24 x +11\right ) x^{\frac {27}{20}} y}{30} = -\frac {a^{2} \left (-1+x \right ) \left (9 x +1\right )}{60 x^{\frac {17}{10}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
30.746 |
|
|
\[ {}y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{\frac {8}{5}}} = \frac {a^{2} \left (-1+x \right ) \left (8 x +1\right )}{5 x^{\frac {11}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.498 |
|
|
\[ {}y y^{\prime }-\frac {6 a \left (1+4 x \right ) y}{5 x^{\frac {7}{5}}} = \frac {a^{2} \left (-1+x \right ) \left (27 x +8\right )}{5 x^{\frac {9}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.306 |
|
|
\[ {}y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{\frac {8}{5}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{\frac {3}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.065 |
|
|
\[ {}y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{\frac {8}{5}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{\frac {11}{5}}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.294 |
|
|
\[ {}y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{\frac {5}{2}}} = \frac {a^{2} \left (-1+x \right ) \left (1+3 x \right )}{2 x^{4}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
3.13 |
|
|
\[ {}y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{\frac {7}{5}}} = \frac {2 a^{2} \left (-1+x \right ) \left (x +4\right )}{5 x^{\frac {9}{5}}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.274 |
|
|
\[ {}y y^{\prime }+\frac {a \left (21 x +19\right ) y}{5 x^{\frac {7}{5}}} = -\frac {2 a^{2} \left (-1+x \right ) \left (9 x -4\right )}{5 x^{\frac {9}{5}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
2.439 |
|
|
\[ {}y y^{\prime }-\frac {3 a y}{x^{\frac {7}{4}}} = \frac {a^{2} \left (-1+x \right ) \left (x -9\right )}{4 x^{\frac {5}{2}}} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
7.648 |
|
|
\[ {}y y^{\prime }-\frac {a \left (\left (k +1\right ) x -1\right ) y}{x^{2}} = \frac {a^{2} \left (k +1\right ) \left (-1+x \right )}{x^{2}} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.105 |
|
|
\[ {}y y^{\prime }-a \left (\left (k -2\right ) x +2 k -3\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (-1+x \right )^{2} x^{1-2 k} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.757 |
|
|
\[ {}y y^{\prime }-\frac {a \left (\left (4 k -7\right ) x -4 k +5\right ) x^{-k} y}{2} = \frac {a^{2} \left (2 k -3\right ) \left (-1+x \right )^{2} x^{1-2 k}}{2} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.814 |
|
|
\[ {}y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-n -1} y = n \left (x -a \right ) x^{-2 n} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.284 |
|
|
\[ {}y y^{\prime }-\left (\left (n +1\right ) x -a n \right ) x^{n -1} \left (x -a \right )^{-n -2} y = n \,x^{2 n} \left (x -a \right )^{-2 n -3} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.543 |
|
|
\[ {}y y^{\prime }-a \left (\left (2 k -3\right ) x +1\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (\left (k -1\right ) x +1\right ) x^{2-2 k} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.473 |
|
|
\[ {}y y^{\prime }-a \left (\left (n +2 k -3\right ) x +3-2 k \right ) x^{-k} y = a^{2} \left (\left (n +k -1\right ) x^{2}-\left (n +2 k -3\right ) x +k -2\right ) x^{1-2 k} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.709 |
|
|
\[ {}y y^{\prime }-\frac {a \left (\left (n +2\right ) x -2\right ) x^{-\frac {1+2 n}{n}} y}{n} = \frac {a^{2} \left (\left (n +1\right ) x^{2}-2 x -n +1\right ) x^{-\frac {3 n +2}{n}}}{n} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.898 |
|
|
\[ {}y y^{\prime }-\frac {a \left (\frac {\left (n +4\right ) x}{n +2}-2\right ) x^{-\frac {1+2 n}{n}} y}{n} = \frac {a^{2} \left (2 x^{2}+\left (n^{2}+n -4\right ) x -\left (n -1\right ) \left (n +2\right )\right ) x^{-\frac {3 n +2}{n}}}{n \left (n +2\right )} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
2.18 |
|
|
\[ {}y y^{\prime }+\frac {a \left (\frac {\left (3 n +5\right ) x}{2}+\frac {n -1}{n +1}\right ) x^{-\frac {n +4}{n +3}} y}{n +3} = -\frac {a^{2} \left (\left (n +1\right ) x^{2}-\frac {\left (n^{2}+2 n +5\right ) x}{n +1}+\frac {4}{n +1}\right ) x^{-\frac {n +5}{n +3}}}{2 n +6} \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
2.401 |
|
|
\[ {}y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y = -\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n} \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.323 |
|
|
\[ {}y y^{\prime } = \left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.419 |
|
|
\[ {}y y^{\prime } = \left (a \left (2 \mu +\lambda \right ) {\mathrm e}^{\lambda x}+b \right ) {\mathrm e}^{\mu x} y+\left (-a^{2} \mu \,{\mathrm e}^{2 \lambda x}-a b \,{\mathrm e}^{\lambda x}+c \right ) {\mathrm e}^{2 \mu x} \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.862 |
|
|
\[ {}y y^{\prime } = \left ({\mathrm e}^{\lambda x} a +b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right ) \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.864 |
|
|
\[ {}y y^{\prime } = {\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right ) \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.523 |
|
|
\[ {}y y^{\prime } = {\mathrm e}^{x a} \left (2 x^{2} a +b +2 x \right ) y+{\mathrm e}^{2 x a} \left (-a \,x^{4}-b \,x^{2}+c \right ) \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
2.412 |
|
|
\[ {}y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y = -a^{2} b \,x^{2} {\mathrm e}^{2 b x} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.095 |
|
|
\[ {}y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.917 |
|
|
\[ {}y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y = -a^{2} b \,x^{\frac {3}{2}} {\mathrm e}^{4 b \sqrt {x}} \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
3.027 |
|
|
\[ {}y y^{\prime } = \left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
2.025 |
|
|
\[ {}y y^{\prime } = \left (a \sinh \left (x \right )+b \right ) y-a b \cosh \left (x \right )+c \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
2.021 |
|
|
\[ {}y y^{\prime } = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right ) \] |
1 |
0 |
1 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.799 |
|
|
\[ {}y y^{\prime } = \left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right ) \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.852 |
|
|
\[ {}y y^{\prime } = a x \cos \left (\lambda \,x^{2}\right ) y+x \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.209 |
|
|
\[ {}y y^{\prime } = a x \sin \left (\lambda \,x^{2}\right ) y+x \] |
1 |
0 |
0 |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.153 |
|
|
\[ {}\left (y+a k \,x^{2}+b x +c \right ) y^{\prime } = -a y^{2}+2 a k x y+m y+k \left (k +b -m \right ) x +s \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
3.752 |
|
|
\[ {}\left (y+x^{n +1} a +b \,x^{n}\right ) y^{\prime } = \left (a n \,x^{n}+c \,x^{n -1}\right ) y \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.812 |
|
|
\[ {}x y y^{\prime } = a y^{2}+b y+c \,x^{n}+s \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
0.885 |
|
|
\[ {}x y y^{\prime } = -n y^{2}+a \left (1+2 n \right ) x y+b y-a^{2} n \,x^{2}-a b x +c \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.083 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.405 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.848 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
N/A |
0.554 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.72 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.701 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 n y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.64 |
|
|
\[ {}y^{\prime \prime }+a x y^{\prime }+b y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.744 |
|
|
\[ {}y^{\prime \prime }+a x y^{\prime }+b x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.579 |
|
|
\[ {}y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.644 |
|
|
\[ {}y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.033 |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+\left (c x +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.722 |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b x +1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.161 |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.847 |
|
|
\[ {}y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+x^{n +1} a +b \,x^{n}+n \,x^{n -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.873 |
|
|
\[ {}y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.248 |
|
|
\[ {}y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.218 |
|
|
\[ {}y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.162 |
|
|
\[ {}y^{\prime \prime }+a \,x^{n} y^{\prime }-b \left (a \,x^{m +n}+b \,x^{2 m}+m \,x^{m -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.09 |
|
|
\[ {}y^{\prime \prime }+2 a \,x^{n} y^{\prime }+\left (a^{2} x^{2 n}+b \,x^{2 m}+a n \,x^{n -1}+c \,x^{m -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.517 |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}+b -c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.55 |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{n}+2 b \right ) y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}+b^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.268 |
|
|
\[ {}y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{n}+1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.256 |
|
|
\[ {}y^{\prime \prime }+\left (a b \,x^{n}+2 b \,x^{n -1}-x \,a^{2}\right ) y^{\prime }+a \left (a b \,x^{n}+b \,x^{n -1}-x \,a^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.27 |
|
|
\[ {}y^{\prime \prime }+x^{n} \left (x^{2} a +\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (x a +b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.884 |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+c \left (a \,x^{n}+b \,x^{m}-c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
52.521 |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}\right ) y^{\prime }+\left (a b \,x^{m +n}+b \left (1+m \right ) x^{m -1}-a \,x^{n -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.757 |
|
|
\[ {}y^{\prime \prime }+\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }+\left (a b \,x^{m +n}+b c \,x^{m}+a n \,x^{n -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.428 |
|
|
\[ {}x y^{\prime \prime }+\left (-x +b \right ) y^{\prime }-a y = 0 \] |
1 |
0 |
1 |
[_Laguerre] |
✗ |
N/A |
0.988 |
|
|
\[ {}x y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c \left (\left (a -c \right ) x +b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.25 |
|
|
\[ {}x y^{\prime \prime }+\left (x \left (a +b \right )+m +n \right ) y^{\prime }+\left (a b x +a n +b m \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.513 |
|
|
\[ {}x y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+\left (c x +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.671 |
|
|
\[ {}x y^{\prime \prime }-\left (2 x a +1\right ) y^{\prime }+b \,x^{3} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.076 |
|
|
\[ {}x y^{\prime \prime }+\left (a b \,x^{2}+b -5\right ) y^{\prime }+2 a^{2} \left (b -2\right ) x^{3} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.941 |
|
|
\[ {}x y^{\prime \prime }+\left (x^{2} a +b x +c \right ) y^{\prime }+\left (A \,x^{2}+B x +\operatorname {C0} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.52 |
|
|
\[ {}x y^{\prime \prime }+\left (x^{2} a +b x +2\right ) y^{\prime }+\left (c \,x^{2}+d x +b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.083 |
|
|
\[ {}x y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n}-a \,x^{n -1}-b^{2} x +2 b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.726 |
|
|
\[ {}x y^{\prime \prime }+\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.747 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.408 |
|
|
\[ {}x y^{\prime \prime }+\left (a b \,x^{n}+b -3 n +1\right ) y^{\prime }+a^{2} n \left (b -n \right ) x^{2 n -1} y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.289 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{2 n -1}+d \,x^{n -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.921 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{n}+b \,x^{n -1}+2\right ) y^{\prime }+b \,x^{n -2} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.186 |
|
|
\[ {}x y^{\prime \prime }+\left (a \,x^{n}+b x \right ) y^{\prime }+\left (a b \,x^{n}+a n \,x^{n -1}-b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.628 |
|
|
\[ {}x y^{\prime \prime }+\left (a b \,x^{n}+b \,x^{n -1}+x a -1\right ) y^{\prime }+a^{2} b \,x^{n} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.165 |
|
|
\[ {}x y^{\prime \prime }+\left (a b \,x^{m +n}+a n \,x^{n}+b \,x^{m}+1-2 n \right ) y^{\prime }+a^{2} b n \,x^{2 n +m -1} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.014 |
|
|
\[ {}\left (a_{1} x +a_{0} \right ) y^{\prime \prime }+\left (b_{1} x +b_{0} \right ) y^{\prime }-m b_{1} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.706 |
|
|
\[ {}\left (x a +b \right ) y^{\prime \prime }+s \left (c x +d \right ) y^{\prime }-s^{2} \left (\left (a +c \right ) x +b +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.187 |
|
|
\[ {}\left (a_{2} x +b_{2} \right ) y^{\prime \prime }+\left (a_{1} x +b_{1} \right ) y^{\prime }+\left (a_{0} x +b_{0} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.505 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (a \,x^{2 n} \left (b \,x^{n}+c \right )^{m}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.911 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.07 |
|
|
\[ {}x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+\left (b \,x^{2}+c x +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.283 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2} a +b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{2}+b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.783 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+\left (k \left (a -k \right ) x^{2}+\left (a n +b k -2 k n \right ) x +n \left (-n +b -1\right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.49 |
|
|
\[ {}a_{2} x^{2} y^{\prime \prime }+\left (a_{1} x^{2}+b_{1} x \right ) y^{\prime }+\left (a_{0} x^{2}+b_{0} x +c_{0} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.445 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.608 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2} a +b x +c \right ) y^{\prime }+\left (A \,x^{3}+B \,x^{2}+C x +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.797 |
|
|
\[ {}x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a b \,x^{n}+a c \,x^{n -1}+b^{2} x^{2}+2 c b x +c^{2}-c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.049 |
|
|
\[ {}x^{2} y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (a b \,x^{n +2 m}-b^{2} x^{4 m +2}+a m \,x^{n -1}-m^{2}-m \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.735 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (a \,x^{n}+b \right ) y^{\prime }+\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.913 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 a \,x^{n}+b \right ) y^{\prime }+\left (a^{2} x^{2 n}+a \left (b +n -1\right ) x^{n}+\alpha \,x^{2 m}+\beta \,x^{m}+\gamma \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.336 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (a \,x^{n +2}+b \,x^{2}+c \right ) y^{\prime }+\left (a n \,x^{n +1}+a c \,x^{n}+b c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.882 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
0.887 |
|
|
\[ {}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+b y^{\prime }-6 y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.639 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.165 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\nu \left (\nu +1\right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.163 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (\nu +n +1\right ) \left (\nu -n \right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.769 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (\nu -n +1\right ) \left (\nu +n \right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.716 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+\left (2 a +1\right ) y^{\prime }-b \left (2 a +b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.345 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (2 a -3\right ) x y^{\prime }+\left (n +1\right ) \left (n +2 a -1\right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
1.642 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\beta -\alpha -\left (\alpha +\beta +2\right ) x \right ) y^{\prime }+n \left (n +\alpha +\beta +1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.938 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\alpha -\beta +\left (\alpha +\beta -2\right ) x \right ) y^{\prime }+\left (n +1\right ) \left (n +\alpha +\beta \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.772 |
|
|
\[ {}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
66.496 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime \prime }+\left (1+2 n \right ) a x y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
233.141 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\left (2 x^{2} a +b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.616 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (x a +b \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.621 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime \prime }+\left (c \,x^{2}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{2}+d -b \lambda \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.193 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime \prime }+\left (\lambda \left (a +c \right ) x^{2}+\left (c -a \right ) x +2 b \lambda \right ) y^{\prime }+\lambda ^{2} \left (c \,x^{2}+b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.278 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x -\gamma \right ) y^{\prime }+\alpha \beta y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
1.944 |
|
|
\[ {}x \left (x +a \right ) y^{\prime \prime }+\left (b x +c \right ) y^{\prime }+d y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.954 |
|
|
\[ {}2 x \left (-1+x \right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (x a +b \right ) y = 0 \] |
1 |
0 |
1 |
[_Jacobi] |
✗ |
N/A |
1.126 |
|
|
\[ {}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime \prime }+\left (b_{1} x +c_{1} \right ) y^{\prime }+c_{0} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.867 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime \prime }-\left (-k^{2}+x^{2}\right ) y^{\prime }+\left (x +k \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
8.194 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime \prime }+\left (k^{3}+x^{3}\right ) y^{\prime }-\left (k^{2}-k x +x^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.444 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (x^{2} a +b \right ) y^{\prime }+c x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.263 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+b y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.944 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.894 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (x^{2} a +b x \right ) y^{\prime }+\left (c x +d \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.191 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (a \,x^{3}+a b x -x^{2}+b \right ) y^{\prime }+a^{2} b x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.567 |
|
|
\[ {}x^{3} y^{\prime \prime }+x \left (a \,x^{n}+b \right ) y^{\prime }-\left (a \,x^{n}-a b \,x^{n -1}+b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.01 |
|
|
\[ {}x \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) y^{\prime }+s x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.221 |
|
|
\[ {}x^{2} \left (x a +b \right ) y^{\prime \prime }+\left (c \,x^{2}+\left (a \lambda +2 b \right ) x +b \lambda \right ) y^{\prime }+\lambda \left (c -2 a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.557 |
|
|
\[ {}x^{2} \left (x +a_{2} \right ) y^{\prime \prime }+x \left (b_{1} x +a_{1} \right ) y^{\prime }+\left (b_{0} x +a_{0} \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.182 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }+\left (\beta -2 b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
8.702 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +2 c \right ) y^{\prime }-\left (\alpha x +2 b -\beta \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.763 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (-2 x^{2} a -\left (b +1\right ) x +k \right ) y^{\prime }+2 \left (x a +1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
35.024 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (k -1\right ) \left (\left (-a k +n \right ) x +m -b k \right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
64.142 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (\left (m -a \right ) x^{2}+\left (2 c m -1\right ) x -c \right ) y^{\prime }+\left (-2 m x +1\right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
366.355 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (-2 \left (a +n \right ) x +1\right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
83.315 |
|
|
\[ {}\left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
16.608 |
|
|
\[ {}x \left (x^{2} a +b x +1\right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\beta x +\gamma \right ) y^{\prime }+\left (n x +m \right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
64.799 |
|
|
\[ {}x \left (-1+x \right ) \left (x -a \right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +d \right )-a \right ) x +a \gamma \right ) y^{\prime }+\left (\alpha \beta x -q \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.546 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
166.434 |
|
|
\[ {}2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+3 \left (3 x^{2} a +2 b x +c \right ) y^{\prime }+\left (6 x a +2 b +\lambda \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
8.111 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\alpha \,x^{2}+\left (\alpha \gamma +\beta \right ) x +\beta \lambda \right ) y^{\prime }-\left (\alpha x +\beta \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
419.376 |
|
|
\[ {}\left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (\lambda ^{3}+x^{3}\right ) y^{\prime }-\left (\lambda ^{2}-\lambda x +x^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
517.49 |
|
|
\[ {}2 x \left (x^{2} a +b x +c \right ) y^{\prime \prime }+\left (a \left (2-k \right ) x^{2}+b \left (1-k \right ) x -c k \right ) y^{\prime }+\lambda \,x^{k +1} y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.216 |
|
|
\[ {}x^{4} y^{\prime \prime }+a \,x^{n} y^{\prime }-\left (a \,x^{n -1}+a b \,x^{n -2}+b^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.933 |
|
|
\[ {}x^{2} \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) x y^{\prime }+d y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.129 |
|
|
\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }-\left (\nu \left (\nu +1\right ) \left (x^{2}-1\right )+n^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.765 |
|
|
\[ {}\left (-x^{2}+1\right )^{2} y^{\prime \prime }-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (\nu \left (\nu +1\right ) \left (-x^{2}+1\right )-\mu ^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.744 |
|
|
\[ {}a \left (x^{2}-1\right )^{2} y^{\prime \prime }+b x \left (x^{2}-1\right ) y^{\prime }+\left (c \,x^{2}+d x +e \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.72 |
|
|
\[ {}\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.716 |
|
|
\[ {}\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.651 |
|
|
\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }+\left (\left (x^{2}-1\right ) \left (a^{2} x^{2}-\lambda \right )-m^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.513 |
|
|
\[ {}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+\left (\left (x^{2}+1\right ) \left (a^{2} x^{2}-\lambda \right )+m^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.656 |
|
|
\[ {}x^{n} y^{\prime \prime }+c \left (x a +b \right )^{n -4} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.253 |
|
|
\[ {}x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.317 |
|
|
\[ {}x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.408 |
|
|
\[ {}x^{n} y^{\prime \prime }+\left (2 x^{n -1}+x^{2} a +b x \right ) y^{\prime }+b y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.732 |
|
|
\[ {}x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.721 |
|
|
\[ {}x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+a^{2} b x y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
5.811 |
|
|
\[ {}x^{n} y^{\prime \prime }+\left (a \,x^{m +n}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.237 |
|
|
\[ {}\left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -b \lambda \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
3.653 |
|
|
\[ {}x \left (x^{n}+1\right ) y^{\prime \prime }+\left (\left (-b +a \right ) x^{n}+a -n \right ) y^{\prime }+b \left (1-a \right ) x^{n -1} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.2 |
|
|
\[ {}x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a^{2} \left (n +1\right ) x^{2 n}+n -1\right ) y^{\prime }-\nu \left (\nu +1\right ) a^{2} n^{2} x^{2 n} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.823 |
|
|
\[ {}x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
25.5 |
|
|
\[ {}\left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{n -2} \left (b \,x^{1+m}+a n -a \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.524 |
|
|
\[ {}\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-a n \,x^{n -1}-1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
5.746 |
|
|
\[ {}x^{2} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (n +1\right ) x \left (a^{2} x^{2 n}-b^{2}\right ) y^{\prime }+c y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.183 |
|
|
\[ {}\left (x^{n +1} a +b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-n b +\beta \right ) x^{n -2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
42.981 |
|
|
\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.868 |
|
|
\[ {}2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+d y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
6.141 |
|
|
\[ {}y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.367 |
|
|
\[ {}y^{\prime \prime }-\left (a^{2} {\mathrm e}^{2 x}+a \left (2 b +1\right ) {\mathrm e}^{x}+b^{2}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.657 |
|
|
\[ {}y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.771 |
|
|
\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{4 \lambda x}+b \,{\mathrm e}^{3 \lambda x}+c \,{\mathrm e}^{2 \lambda x}-\frac {\lambda ^{2}}{4}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.735 |
|
|
\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.173 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.756 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.355 |
|
|
\[ {}y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.825 |
|
|
\[ {}y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{\mu x} \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}+\mu \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.651 |
|
|
\[ {}y^{\prime \prime }+2 k \,{\mathrm e}^{\mu x} y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 \mu x}+k \mu \,{\mathrm e}^{\mu x}+c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.574 |
|
|
\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.309 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+c \left ({\mathrm e}^{\lambda x} a +b -c \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.085 |
|
|
\[ {}y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.976 |
|
|
\[ {}y^{\prime \prime }+\left (a +b \,{\mathrm e}^{\lambda x}+b -3 \lambda \right ) y^{\prime }+a^{2} \lambda \left (b -\lambda \right ) {\mathrm e}^{2 \lambda x} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.493 |
|
|
\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{\mu x}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.232 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+b^{2}-b \lambda \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.39 |
|
|
\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.309 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.314 |
|
|
\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 \mu x}+c \,{\mathrm e}^{\mu x}+k \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.483 |
|
|
\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \mu x}+d \,{\mathrm e}^{\mu x}+k \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.063 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\mu x}+\lambda \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.641 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.911 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{\mu x}\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.794 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right ) = \left (x^{2}+y^{2}+x \right ) \left (-y+x y^{\prime }\right ) \] |
1 |
0 |
1 |
[_rational] |
✗ |
N/A |
1.308 |
|
|
\[ {}x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
1.693 |
|
|
\[ {}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0 \] |
2 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
4.438 |
|
|
|
||||||||
|
\[ {}{\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x} = 0 \] |
3 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
204.26 |
|
|
\[ {}\left (x -y^{\prime }-y\right )^{2} = x^{2} \left (2 x y-x^{2} y^{\prime }\right ) \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
5.846 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = x^{2} y^{2}+x^{4} \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
3.427 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.31 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.427 |
|
|
\[ {}x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.026 |
|
|
\[ {}\left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2} = {y^{\prime \prime \prime }}^{2}+1 \] |
1 |
1 |
3 |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.09 |
|
|
\[ {}x y^{\prime \prime \prime }-y^{\prime \prime }-x y^{\prime }+y = -x^{2}+1 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.133 |
|
|
\[ {}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
N/A |
0.408 |
|
|
\[ {}2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 x y y^{\prime }+6 y^{2} = 0 \] |
1 |
1 |
3 |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
73.061 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.345 |
|
|
\[ {}x^{2} y y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{2} = 0 \] |
1 |
0 |
3 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.097 |
|
|
\[ {}x^{3} y^{\prime \prime }-\left (-y+x y^{\prime }\right )^{2} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.108 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )-x^{2} y^{2} \] |
1 |
0 |
1 |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
N/A |
0.097 |
|
|
\[ {}\sin \left (x \right )^{2} y^{\prime \prime }-2 y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.161 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
N/A |
0.476 |
|
|
\[ {}x x^{\prime } = 1-x t \] |
1 |
0 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.551 |
|
|
\[ {}{x^{\prime }}^{2}+x t = \sqrt {t +1} \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.834 |
|
|
\[ {}3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
0.874 |
|
|
\[ {}\frac {2 y^{\frac {3}{2}}+1}{x^{\frac {1}{3}}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
45.935 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.577 |
|
|
\[ {}{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1 \] |
2 |
2 |
3 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}m x^{\prime \prime } = f \left (x\right ) \] |
1 |
0 |
2 |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
N/A |
0.407 |
|
|
\[ {}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \] |
2 |
2 |
2 |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime } = \sin \left (x y\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.618 |
|
|
\[ {}y^{\prime } = t \ln \left (y^{2 t}\right )+t^{2} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.602 |
|
|
\[ {}y^{\prime } = \ln \left (x y\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.337 |
|
|
\[ {}y^{\prime \prime \prime }+x y = \sin \left (x \right ) \] |
1 |
0 |
1 |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.229 |
|
|
\[ {}y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1 \] |
1 |
1 |
1 |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime }+x y = \cosh \left (x \right ) \] |
1 |
0 |
1 |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.244 |
|
|
\[ {}y^{\prime \prime \prime }+x y = \cosh \left (x \right ) \] |
1 |
0 |
1 |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.235 |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1 \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.86 |
|
|
\[ {}y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right ) \] |
1 |
1 |
0 |
[NONE] |
✗ |
N/A |
0.0 |
|
|
\[ {}{y^{\prime }}^{2}+x y {y^{\prime }}^{2} = \ln \left (x \right ) \] |
2 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.12 |
|
|
\[ {}\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1 \] |
1 |
1 |
1 |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.172 |
|
|
\[ {}{y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right ) \] |
1 |
1 |
0 |
[NONE] |
✗ |
N/A |
0.0 |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2} \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.365 |
|
|
\[ {}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cot \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.31 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.842 |
|
|
\[ {}x y^{\prime \prime }+2 x^{2} y^{\prime }+y \sin \left (x \right ) = \sinh \left (x \right ) \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
4.067 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
73.85 |
|
|
\[ {}y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+x^{2} y = \tan \left (x \right ) \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
1.026 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.622 |
|
|
\[ {}y^{\prime \prime }+\frac {k x}{y^{4}} = 0 \] |
1 |
0 |
2 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.156 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.669 |
|
|
\[ {}\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.005 |
|
|
\[ {}\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right ) = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.687 |
|
|
\[ {}y^{\prime \prime }+\frac {\left (-1+x \right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.661 |
|
|
\[ {}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right ) \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
3.346 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.377 |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right ) \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.88 |
|
|
\[ {}t^{3} y^{\prime \prime }-2 t y^{\prime }+y = t^{4} \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.51 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0 \] |
1 |
0 |
1 |
[_Gegenbauer] |
✗ |
N/A |
0.945 |
|
|
\[ {}y^{\prime } \left (x^{2} y^{3}+x y\right ) = 1 \] |
1 |
0 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
N/A |
1.272 |
|
|
\[ {}y^{\prime \prime \prime } = {y^{\prime \prime }}^{2} \] |
1 |
1 |
1 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0 \] |
1 |
1 |
3 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}} \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.855 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x} \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.964 |
|
|
\[ {}y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \] |
1 |
0 |
0 |
[‘x=_G(y,y’)‘] |
✗ |
N/A |
3.796 |
|
|
\[ {}y^{2} y^{\prime \prime } = 8 x^{2} \] |
1 |
0 |
1 |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.096 |
|
|
\[ {}\sin \left (x +y\right )-y y^{\prime } = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.979 |
|
|
\[ {}y^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.335 |
|
|
\[ {}y^{\prime \prime \prime } = 2 \sqrt {y^{\prime \prime }} \] |
1 |
1 |
2 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }-4 y = x^{3} \] |
1 |
0 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
1.017 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }-4 y = 0 \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.801 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime } = 4 y \] |
1 |
0 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.806 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+4 y = y^{3} \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.111 |
|
|
\[ {}y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y \] |
1 |
1 |
2 |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0 \] |
1 |
0 |
1 |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.159 |
|
|
\[ {}t y^{\prime \prime }+y^{\prime }+t y = 0 \] |
1 |
1 |
1 |
[_Lienard] |
✗ |
N/A |
0.0 |
|
|
\[ {}y y^{\prime }+y^{4} = \sin \left (x \right ) \] |
1 |
0 |
2 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.337 |
|
|
\[ {}x {y^{\prime \prime }}^{2}+2 y = 2 x \] |
2 |
0 |
2 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.493 |
|
|
\[ {}x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right ) \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
1.274 |
|
|
\[ {}4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
31.028 |
|
|
\[ {}y^{\prime }+t^{2} = \frac {1}{y^{2}} \] |
1 |
0 |
0 |
[_rational] |
✗ |
N/A |
1.046 |
|
|
\[ {}y^{\prime } = \sin \left (y\right )-\cos \left (t \right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.324 |
|
|
\[ {}{\mathrm e}^{2 t}-y-\left ({\mathrm e}^{y}-t \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.326 |
|
|
\[ {}1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
8.605 |
|
|
\[ {}y^{\prime } = x +y^{\frac {1}{3}} \] |
1 |
0 |
0 |
[_Chini] |
✗ |
N/A |
0.863 |
|
|
\[ {}y^{\prime } = \sin \left (x^{2} y\right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.079 |
|
|
\[ {}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0 \] |
2 |
0 |
3 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.355 |
|
|
\[ {}{y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0 \] |
2 |
0 |
4 |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.314 |
|
|
\[ {}{\mathrm e}^{-2 t} \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )-2 t \left (t +1\right ) y = 0 \] |
1 |
0 |
0 |
[NONE] |
✗ |
N/A |
0.199 |
|
|
\[ {}t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{\frac {7}{2}}} \] |
1 |
0 |
1 |
[[_high_order, _missing_y]] |
✗ |
N/A |
1.443 |
|
|
\[ {}y^{\prime } = \sin \left (y\right )-\cos \left (x \right ) \] |
1 |
0 |
0 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.949 |
|
|
\[ {}y^{\prime } = \sin \left (x y\right ) \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
0.863 |
|
|
\[ {}y^{\prime }-2 \,{\mathrm e}^{x} y = 2 \sqrt {{\mathrm e}^{x} y} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
2.112 |
|
|
\[ {}y^{\prime } = y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
N/A |
1.427 |
|
|
\[ {}y y^{\prime }+1 = \left (-1+x \right ) {\mathrm e}^{-\frac {y^{2}}{2}} \] |
1 |
0 |
2 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.293 |
|
|
\[ {}y^{\prime }+x \sin \left (2 y\right ) = 2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \] |
1 |
0 |
1 |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
3.725 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) y^{2}-4 y y^{\prime }-4 x = 0 \] |
2 |
0 |
4 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.936 |
|
|
\[ {}y^{\prime \prime \prime } = \sqrt {1-{y^{\prime \prime }}^{2}} \] |
1 |
3 |
0 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime }+{y^{\prime \prime }}^{2} = 0 \] |
1 |
3 |
1 |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime } = 3 y y^{\prime } \] |
1 |
3 |
1 |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_x]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime \prime }-\lambda ^{4} y = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_x]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime }+x \sin \left (y\right ) = 0 \] |
1 |
1 |
1 |
[NONE] |
✗ |
N/A |
0.0 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=y \left (t \right ) \\ y^{\prime \prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✗ |
N/A |
|
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )=0 \\ x^{\prime }\left (t \right )+y^{\prime \prime }\left (t \right )=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✗ |
N/A |
|
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✗ |
N/A |
|
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
✗ |
N/A |
|
|
|
|
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|
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