|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {x}{-y+F \left (x^{2}+y^{2}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.194 |
|
|
\[
{}y^{\prime } = \frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.112 |
|
|
\[
{}y^{\prime } = \frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
3.170 |
|
|
\[
{}y^{\prime } = \frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.769 |
|
|
\[
{}y^{\prime } = \frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.997 |
|
|
\[
{}y^{\prime } = \frac {F \left (\frac {x y^{2}+1}{x}\right )}{y x^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.108 |
|
|
\[
{}y^{\prime } = \frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.534 |
|
|
\[
{}y^{\prime } = \frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.635 |
|
|
\[
{}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right )}{x -1}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
1.751 |
|
|
\[
{}y^{\prime } = \frac {-x +F \left (x^{2}+y^{2}\right )}{y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.205 |
|
|
\[
{}y^{\prime } = \frac {F \left (-\frac {-1+2 y \ln \left (x \right )}{y}\right ) y^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
1.582 |
|
|
\[
{}y^{\prime } = \frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.983 |
|
|
\[
{}y^{\prime } = \frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}}
\] |
[NONE] |
✗ |
1.912 |
|
|
\[
{}y^{\prime } = \frac {2 F \left (y+\ln \left (2 x +1\right )\right ) x +F \left (y+\ln \left (2 x +1\right )\right )-2}{2 x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.741 |
|
|
\[
{}y^{\prime } = \frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y}
\] |
[‘x=_G(y,y’)‘] |
✗ |
2.181 |
|
|
\[
{}y^{\prime } = -\frac {y^{2} \left (2 x -F \left (-\frac {x y-2}{2 y}\right )\right )}{4 x}
\] |
[NONE] |
✓ |
2.315 |
|
|
\[
{}y^{\prime } = -\left (-{\mathrm e}^{-x^{2}}+x^{2} {\mathrm e}^{-x^{2}}-F \left (y-\frac {x^{2} {\mathrm e}^{-x^{2}}}{2}\right )\right ) x
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
2.957 |
|
|
\[
{}y^{\prime } = \frac {2 y+F \left (\frac {y}{x^{2}}\right ) x^{3}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.992 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.537 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y+F \left (x^{3} y\right )}{x^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.092 |
|
|
\[
{}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
1.258 |
|
|
\[
{}y^{\prime } = \frac {-2 x -y+F \left (\left (x +y\right ) x \right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.348 |
|
|
\[
{}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
1.945 |
|
|
\[
{}y^{\prime } = \frac {x +y+F \left (-\frac {-y+x \ln \left (x \right )}{x}\right ) x^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.573 |
|
|
\[
{}y^{\prime } = \frac {x \left (a -1\right ) \left (a +1\right )}{y+F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right ) a^{2}-F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.398 |
|
|
\[
{}y^{\prime } = \frac {y}{x \left (-1+F \left (x y\right ) y\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
231.283 |
|
|
\[
{}y^{\prime } = -\frac {-x^{2}+2 x^{3} y-F \left (\left (x y-1\right ) x \right )}{x^{4}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime } = \frac {F \left (\frac {\left (3+y\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{3 y}\right ) x y^{2} {\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
3.176 |
|
|
\[
{}y^{\prime } = \frac {\left (1+y\right ) \left (\left (y-\ln \left (1+y\right )-\ln \left (x \right )\right ) x +1\right )}{y x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.738 |
|
|
\[
{}y^{\prime } = \frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
2.657 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.901 |
|
|
\[
{}y^{\prime } = \frac {1}{y+\sqrt {x}}
\] |
[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.573 |
|
|
\[
{}y^{\prime } = \frac {1}{y+2+\sqrt {1+3 x}}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
5.817 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y+x^{{3}/{2}}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
5.780 |
|
|
\[
{}y^{\prime } = \frac {x^{{5}/{3}}}{y+x^{{4}/{3}}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
5.088 |
|
|
\[
{}y^{\prime } = \frac {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
36.556 |
|
|
\[
{}y^{\prime } = \frac {x}{y+\sqrt {x^{2}+1}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
4.352 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x}
\] |
[_Riccati] |
✓ |
2.464 |
|
|
\[
{}y^{\prime } = \frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
3.077 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{2}}{x}
\] |
[_Riccati] |
✓ |
2.724 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
3.589 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
3.867 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x}}{y \,{\mathrm e}^{-x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
3.572 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
3.306 |
|
|
\[
{}y^{\prime } = \frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
36.536 |
|
|
\[
{}y^{\prime } = \frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.791 |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+x^{2}\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.503 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.513 |
|
|
\[
{}y^{\prime } = -\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y
\] |
[‘x=_G(y,y’)‘] |
✗ |
2.749 |
|
|
\[
{}y^{\prime } = \left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.188 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1}
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.356 |
|
|
\[
{}y^{\prime } = \frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
36.565 |
|
|
\[
{}y^{\prime } = \frac {\left (-y^{2}+4 a x \right )^{2}}{y}
\] |
[_rational] |
✗ |
2.842 |
|
|
\[
{}y^{\prime } = \frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.201 |
|
|
\[
{}y^{\prime } = -\frac {x^{2} \left (a x -2 \sqrt {a \left (a \,x^{4}+8 y\right )}\right )}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
5.631 |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+x \right ) y
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime } = \frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.211 |
|
|
\[
{}y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
3.124 |
|
|
\[
{}y^{\prime } = -\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
6.112 |
|
|
\[
{}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.518 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 a x +a^{2}+4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.375 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.610 |
|
|
\[
{}y^{\prime } = \frac {2 a +x \sqrt {-y^{2}+4 a x}}{y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
37.283 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+1+x \sqrt {x^{2}-4 x +4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.451 |
|
|
\[
{}y^{\prime } = -\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.820 |
|
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.766 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.656 |
|
|
\[
{}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.546 |
|
|
\[
{}y^{\prime } = -\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.503 |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.408 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.374 |
|
|
\[
{}y^{\prime } = -\frac {a x}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.433 |
|
|
\[
{}y^{\prime } = \frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.274 |
|
|
\[
{}y^{\prime } = \frac {2 a +x^{2} \sqrt {-y^{2}+4 a x}}{y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
36.215 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+1+x^{2} \sqrt {x^{2}-4 x +4 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.535 |
|
|
\[
{}y^{\prime } = -\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
37.729 |
|
|
\[
{}y^{\prime } = \left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.657 |
|
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
1.846 |
|
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 x}}{y \,{\mathrm e}^{-x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.705 |
|
|
\[
{}y^{\prime } = \frac {\left (-2 y^{{3}/{2}}+3 \,{\mathrm e}^{x}\right )^{2} {\mathrm e}^{x}}{4 \sqrt {y}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
3.880 |
|
|
\[
{}y^{\prime } = \frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
5.382 |
|
|
\[
{}y^{\prime } = \frac {\left (x y^{2}+1\right )^{2}}{y x^{4}}
\] |
[_rational] |
✗ |
2.644 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
44.662 |
|
|
\[
{}y^{\prime } = \frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{2}+x^{2}}{2 x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.516 |
|
|
\[
{}y^{\prime } = -\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.557 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-x^{2} y^{2}-x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
13.077 |
|
|
\[
{}y^{\prime } = \frac {x +1+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3} \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
6.809 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} a \ln \left (x +1\right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (x +1\right )-x^{2} y^{2}-x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
28.319 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
5.273 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 x^{2} y^{2}+7 x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
5.727 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.526 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+x^{4} b +b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+a \,x^{2} y^{2}+a x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
16.822 |
|
|
\[
{}y^{\prime } = \frac {2 a}{x \left (-x y+2 a x y^{2}-8 a^{2}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.396 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x}
\] |
[_Bernoulli] |
✓ |
5.256 |
|
|
\[
{}y^{\prime } = \frac {y+\sqrt {x^{2}+y^{2}}\, x^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
9.254 |
|
|
\[
{}y^{\prime } = \frac {y+\ln \left (\left (x -1\right ) \left (x +1\right )\right ) x^{3}+7 \ln \left (\left (x -1\right ) \left (x +1\right )\right ) x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.233 |
|
|
\[
{}y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.015 |
|
|
\[
{}y^{\prime } = \frac {y-\ln \left (\frac {x +1}{x -1}\right ) x^{3}+\ln \left (\frac {x +1}{x -1}\right ) x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.139 |
|
|
\[
{}y^{\prime } = \frac {y+{\mathrm e}^{\frac {x +1}{x -1}} x^{3}+{\mathrm e}^{\frac {x +1}{x -1}} x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.658 |
|
|
\[
{}y^{\prime } = \frac {x y-y-{\mathrm e}^{x +1} x^{3}+{\mathrm e}^{x +1} x y^{2}}{\left (x -1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.813 |
|