|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y = 0
\] |
[_quadrature] |
✓ |
0.920 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2}-1 = 0
\] |
[_Clairaut] |
✓ |
7.251 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.882 |
|
|
\[
{}a \,x^{n} f \left (y^{\prime }\right )+y^{\prime } x -y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.589 |
|
|
\[
{}\left (-y+y^{\prime } x \right )^{n} f \left (y^{\prime }\right )+y g \left (y^{\prime }\right )+x h \left (y^{\prime }\right ) = 0
\] |
[‘x=_G(y,y’)‘] |
✓ |
2.561 |
|
|
\[
{}f \left (x {y^{\prime }}^{2}\right )+2 y^{\prime } x -y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.393 |
|
|
\[
{}f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
0.848 |
|
|
\[
{}y^{\prime } f \left (x y y^{\prime }-y^{2}\right )-x^{2} y^{\prime }+y x = 0
\] |
[NONE] |
✓ |
0.526 |
|
|
\[
{}\phi \left (f \left (x , y, y^{\prime }\right ), g \left (x , y, y^{\prime }\right )\right ) = 0
\] |
[NONE] |
✓ |
0.908 |
|
|
\[
{}y^{\prime } = F \left (\frac {y}{x +a}\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.874 |
|
|
\[
{}y^{\prime } = 2 x +F \left (y-x^{2}\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
0.650 |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
0.960 |
|
|
\[
{}y^{\prime } = F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
0.805 |
|
|
\[
{}y^{\prime } = \frac {1+2 F \left (\frac {4 x^{2} y+1}{4 x^{2}}\right ) x}{2 x^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.082 |
|
|
\[
{}y^{\prime } = \frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.128 |
|
|
\[
{}y^{\prime } = -\frac {\left (a \,x^{2}-2 F \left (y+\frac {a \,x^{4}}{8}\right )\right ) x}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.211 |
|
|
\[
{}y^{\prime } = \frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime } = F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.760 |
|
|
\[
{}y^{\prime } = \frac {F \left (\frac {y}{\sqrt {x^{2}+1}}\right ) x}{\sqrt {x^{2}+1}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.748 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{{3}/{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.355 |
|
|
\[
{}y^{\prime } = \frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.034 |
|
|
\[
{}y^{\prime } = \frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
1.469 |
|
|
\[
{}y^{\prime } = \frac {x}{-y+F \left (x^{2}+y^{2}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.150 |
|
|
\[
{}y^{\prime } = \frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.128 |
|
|
\[
{}y^{\prime } = \frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.438 |
|
|
\[
{}y^{\prime } = \frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.350 |
|
|
\[
{}y^{\prime } = \frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.092 |
|
|
\[
{}y^{\prime } = \frac {F \left (\frac {x y^{2}+1}{x}\right )}{y x^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.052 |
|
|
\[
{}y^{\prime } = \frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.533 |
|
|
\[
{}y^{\prime } = \frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.455 |
|
|
\[
{}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right )}{x -1}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
1.628 |
|
|
\[
{}y^{\prime } = \frac {-x +F \left (x^{2}+y^{2}\right )}{y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.140 |
|
|
\[
{}y^{\prime } = \frac {F \left (-\frac {2 y \ln \left (x \right )-1}{y}\right ) y^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
1.445 |
|
|
\[
{}y^{\prime } = \frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.037 |
|
|
\[
{}y^{\prime } = \frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}}
\] |
[NONE] |
✗ |
1.317 |
|
|
\[
{}y^{\prime } = \frac {2 F \left (y+\ln \left (2 x +1\right )\right ) x +F \left (y+\ln \left (2 x +1\right )\right )-2}{2 x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.305 |
|
|
\[
{}y^{\prime } = \frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y}
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.269 |
|
|
\[
{}y^{\prime } = -\frac {y^{2} \left (2 x -F \left (-\frac {-2+y x}{2 y}\right )\right )}{4 x}
\] |
[NONE] |
✓ |
2.201 |
|
|
\[
{}y^{\prime } = -\left (-{\mathrm e}^{-x^{2}}+x^{2} {\mathrm e}^{-x^{2}}-F \left (y-\frac {x^{2} {\mathrm e}^{-x^{2}}}{2}\right )\right ) x
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.379 |
|
|
\[
{}y^{\prime } = \frac {2 y+F \left (\frac {y}{x^{2}}\right ) x^{3}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.029 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.513 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y+F \left (x^{3} y\right )}{x^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.112 |
|
|
\[
{}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
1.175 |
|
|
\[
{}y^{\prime } = \frac {-2 x -y+F \left (\left (x +y\right ) x \right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.167 |
|
|
\[
{}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.088 |
|
|
\[
{}y^{\prime } = \frac {x +y+F \left (-\frac {-y+x \ln \left (x \right )}{x}\right ) x^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.302 |
|
|
\[
{}y^{\prime } = \frac {x \left (a -1\right ) \left (a +1\right )}{y+F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right ) a^{2}-F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.375 |
|
|
\[
{}y^{\prime } = \frac {y}{x \left (-1+F \left (y x \right ) y\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
198.367 |
|
|
\[
{}y^{\prime } = -\frac {-x^{2}+2 x^{3} y-F \left (\left (y x -1\right ) x \right )}{x^{4}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.466 |
|
|
\[
{}y^{\prime } = \frac {F \left (\frac {\left (3+y\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{3 y}\right ) x y^{2} {\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.645 |
|
|
\[
{}y^{\prime } = \frac {\left (1+y\right ) \left (\left (y-\ln \left (1+y\right )-\ln \left (x \right )\right ) x +1\right )}{y x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.739 |
|
|
\[
{}y^{\prime } = \frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.494 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.806 |
|
|
\[
{}y^{\prime } = \frac {1}{y+\sqrt {x}}
\] |
[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.403 |
|
|
\[
{}y^{\prime } = \frac {1}{y+2+\sqrt {3 x +1}}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
5.300 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y+x^{{3}/{2}}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
5.500 |
|
|
\[
{}y^{\prime } = \frac {x^{{5}/{3}}}{y+x^{{4}/{3}}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
4.873 |
|
|
\[
{}y^{\prime } = \frac {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.179 |
|
|
\[
{}y^{\prime } = \frac {x}{y+\sqrt {x^{2}+1}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
3.320 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x}
\] |
[_Riccati] |
✓ |
2.344 |
|
|
\[
{}y^{\prime } = \frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.958 |
|
|
\[
{}y^{\prime } = \frac {\left (2 y \ln \left (x \right )-1\right )^{2}}{x}
\] |
[_Riccati] |
✓ |
2.581 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
3.363 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
3.592 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x}}{y \,{\mathrm e}^{-x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
3.384 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.982 |
|
|
\[
{}y^{\prime } = \frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.723 |
|
|
\[
{}y^{\prime } = \frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.617 |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+x^{2}\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.321 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.276 |
|
|
\[
{}y^{\prime } = -\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.431 |
|
|
\[
{}y^{\prime } = \left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.685 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.651 |
|
|
\[
{}y^{\prime } = \frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.739 |
|
|
\[
{}y^{\prime } = \frac {\left (-y^{2}+4 a x \right )^{2}}{y}
\] |
[_rational] |
✗ |
1.449 |
|
|
\[
{}y^{\prime } = \frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.017 |
|
|
\[
{}y^{\prime } = -\frac {x^{2} \left (a x -2 \sqrt {a \left (a \,x^{4}+8 y\right )}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.967 |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+x \right ) y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
0.986 |
|
|
\[
{}y^{\prime } = \frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.095 |
|
|
\[
{}y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.669 |
|
|
\[
{}y^{\prime } = -\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
2.205 |
|
|
\[
{}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.401 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 a x +a^{2}+4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.308 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.395 |
|
|
\[
{}y^{\prime } = \frac {2 a +x \sqrt {-y^{2}+4 a x}}{y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
68.647 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+1+x \sqrt {x^{2}-4 x +4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.455 |
|
|
\[
{}y^{\prime } = -\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.632 |
|
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.619 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.406 |
|
|
\[
{}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.433 |
|
|
\[
{}y^{\prime } = -\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.406 |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.457 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.221 |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.359 |
|
|
\[
{}y^{\prime } = \frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.198 |
|
|
\[
{}y^{\prime } = \frac {2 a +x^{2} \sqrt {-y^{2}+4 a x}}{y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
67.492 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+1+x^{2} \sqrt {x^{2}-4 x +4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.766 |
|
|
\[
{}y^{\prime } = -\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
2.138 |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.467 |
|
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
1.772 |
|