These are ode’s of the form \(f(y)dy = h(x)dx w(y)dy\) where the RHS is a complete differential transformaing the ode to \(f(y)dy = d( g(x,y) )\) and then the ode is solved by integrating both sides. As an example of such is \[ \frac {d}{d x}y \left (x \right ) = \frac {y \left (x \right )}{2 y \left (x \right ) \ln \left (y \left (x \right )\right )+y \left (x \right )-x} \] Number of problems in this table is 254
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) |
|
\[ {}y y^{\prime } = -1+x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.47 |
|
|
\[ {}y y^{\prime } = -1+x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.789 |
|
|
\[ {}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
170.809 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.521 |
|
|
\[ {}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.327 |
|
|
\[ {}4 x -y+\left (-x +6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.744 |
|
|
\[ {}y^{\prime } = \frac {x +3 y}{-3 x +y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.993 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.209 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}-1}{3+2 y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.528 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{1+y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
154.618 |
|
|
\[ {}y^{\prime } = \frac {1-2 x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.71 |
|
|
\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.693 |
|
|
\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.85 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.06 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
78.154 |
|
|
\[ {}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
168.757 |
|
|
\[ {}y^{\prime } = -\frac {4 t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.775 |
|
|
\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.759 |
|
|
\[ {}2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
18.126 |
|
|
\[ {}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.071 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.527 |
|
|
\[ {}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.914 |
|
|
\[ {}-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
8.075 |
|
|
\[ {}1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.234 |
|
|
\[ {}\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
2.105 |
|
|
\[ {}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
14.87 |
|
|
\[ {}y^{\prime } = \frac {y+2 x}{3-x +3 y^{2}} \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
280.432 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
89.541 |
|
|
\[ {}y^{\prime } = \frac {-1-2 x y}{x^{2}+2 y} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.277 |
|
|
\[ {}x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact] |
✓ |
✓ |
3.525 |
|
|
\[ {}x +y+\left (2 y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.832 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-1}{1+y^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
67.306 |
|
|
\[ {}x y^{\prime }+y = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.024 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+4 x y = \frac {2}{x^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.988 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}+2 x +1}{y-2} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.806 |
|
|
\[ {}\left (y-1\right )^{2} y^{\prime } = 2 x +3 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
21.325 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+3 x +2}{y-2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.9 |
|
|
\[ {}y^{\prime } = \frac {2 x}{1+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.329 |
|
|
\[ {}x +y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.77 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.012 |
|
|
\[ {}\left (2 x -1\right ) \left (y-1\right )+\left (2+x \right ) \left (x -3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.746 |
|
|
\[ {}7 x +4 y+\left (4 x +3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
|
\[ {}3 x^{2}+2 y+\left (2 y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.579 |
|
|
\[ {}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.446 |
|
|
\[ {}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.358 |
|
|
\[ {}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.778 |
|
|
\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.261 |
|
|
\[ {}3 t^{2}+4 t y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.358 |
|
|
\[ {}x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.438 |
|
|
\[ {}\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.84 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-1+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.157 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.742 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.781 |
|
|
\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.725 |
|
|
\[ {}x -y+\left (-x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.164 |
|
|
\[ {}x +y+\left (x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.179 |
|
|
\[ {}3 x +y+\left (x +3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.376 |
|
|
\[ {}x \left (6 x y+5\right )+\left (2 x^{3}+3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.313 |
|
|
\[ {}\left (1-x \right ) y^{\prime }-y-1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.467 |
|
|
\[ {}y^{\prime } \sin \left (y\right ) = x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.825 |
|
|
\[ {}y^{\prime } = -\frac {t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.953 |
|
|
\[ {}t y^{\prime } = -y+t^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}y^{\prime }+\frac {2 x y}{x^{2}+1} = 4 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.722 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.762 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.622 |
|
|
\[ {}3 y-2 x +\left (-2+3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}\left (x +y^{2}\right ) y^{\prime }+y-x^{2} = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
68.71 |
|
|
\[ {}y y^{\prime } = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.506 |
|
|
\[ {}x y^{\prime }+y = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.986 |
|
|
\[ {}3 y^{2} y^{\prime } = 2 x -1 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
9.704 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}\left (x +y-1\right ) y^{\prime } = x -y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.594 |
|
|
\[ {}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
1.237 |
|
|
\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = 4 x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.955 |
|
|
\[ {}3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.217 |
|
|
\[ {}1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
4.974 |
|
|
\[ {}x y^{\prime }+x +y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.751 |
|
|
\[ {}x y^{\prime } = x^{3}-y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.597 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.527 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.632 |
|
|
\[ {}x \left (-x^{3}+1\right ) y^{\prime } = 2 x -\left (-4 x^{3}+1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.726 |
|
|
\[ {}x +y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.987 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.407 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.351 |
|
|
\[ {}\left (2+x +y\right ) y^{\prime } = 1-x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.888 |
|
|
\[ {}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.998 |
|
|
\[ {}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.981 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime }+2 x +y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.19 |
|
|
\[ {}\left (1+x -2 y\right ) y^{\prime } = 1+2 x -y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.033 |
|
|
\[ {}2 \left (x +y\right ) y^{\prime }+x^{2}+2 y = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.186 |
|
|
\[ {}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.346 |
|
|
\[ {}\left (x^{3}+2 y\right ) y^{\prime } = 3 x \left (2-x y\right ) \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.348 |
|
|
\[ {}\left (5+2 x -4 y\right ) y^{\prime } = 3+x -2 y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.953 |
|
|
\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.467 |
|
|
\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.115 |
|
|
\[ {}\left (x -y^{2}\right ) y^{\prime } = x^{2}-y \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
9.654 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (2 y+x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
7.746 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
9.385 |
|
|
\[ {}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
8.592 |
|
|
\[ {}y \left (y+1\right ) y^{\prime } = \left (1+x \right ) x \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
165.359 |
|
|
\[ {}\left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
10.477 |
|
|
\[ {}\left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 x y = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
9.799 |
|
|
\[ {}\left (3 x -y^{3}\right ) y^{\prime } = x^{2}-3 y \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
1.135 |
|
|
\[ {}y \left (2 y^{2}+1\right ) y^{\prime } = x \left (2 x^{2}+1\right ) \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
2.901 |
|
|
\[ {}y^{\prime } \sqrt {y} = \sqrt {x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
166.565 |
|
|
\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
9.542 |
|
|
\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.572 |
|
|
\[ {}x y^{\prime }+y = x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.864 |
|
|
\[ {}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.098 |
|
|
\[ {}\left (1+x^{2}+y^{2}\right ) y^{\prime }+2 x y+x^{2}+3 = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
14.271 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
12.457 |
|
|
\[ {}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
4.438 |
|
|
\[ {}\frac {x}{y+1} = \frac {y y^{\prime }}{1+x} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
177.621 |
|
|
\[ {}\left (x -y\right ) y^{\prime }+1+x +y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.817 |
|
|
\[ {}\left (y+2 x \right ) y^{\prime }-x +2 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.436 |
|
|
\[ {}x^{2}+2 y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.619 |
|
|
\[ {}x^{2} y^{\prime }+2 x y-x +1 = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.41 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.437 |
|
|
\[ {}y^{\prime } = \frac {1+x -2 y}{2 x -4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.503 |
|
|
\[ {}y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y = \frac {1}{-x^{2}+1} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.244 |
|
|
\[ {}x +y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.714 |
|
|
\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.096 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{1-y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
164.3 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}+4 x +2}{-2+2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.204 |
|
|
\[ {}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
12.398 |
|
|
\[ {}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.178 |
|
|
\[ {}x y^{\prime }+y = 3 x^{3}-1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.842 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.868 |
|
|
\[ {}y y^{\prime } = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.651 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x}{y-y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
172.495 |
|
|
\[ {}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
2.069 |
|
|
\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.158 |
|
|
\[ {}x y^{\prime }+y = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.171 |
|
|
\[ {}y^{2} y^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
163.036 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.173 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.537 |
|
|
\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.548 |
|
|
\[ {}y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {y^{2}-1}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.974 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y-2 x^{2} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.036 |
|
|
\[ {}\left (-x +2 y\right ) y^{\prime }-y-2 x = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.146 |
|
|
\[ {}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.281 |
|
|
\[ {}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
|
\[ {}\left (-x +y^{2}\right ) y^{\prime }-y+x^{2} = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
12.393 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
10.35 |
|
|
\[ {}\left (y^{2}+x^{2}+a \right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
3 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
10.403 |
|
|
\[ {}\left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2} = 0 \] |
1 |
1 |
1 |
[_exact, _rational] |
✓ |
✓ |
1.838 |
|
|
\[ {}2 y^{3} y^{\prime }+x y^{2} = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
2.089 |
|
|
\[ {}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
4.007 |
|
|
\[ {}\sqrt {y^{2}-1}\, y^{\prime }-\sqrt {x^{2}-1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.625 |
|
|
\[ {}x y^{\prime }+x +y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.278 |
|
|
\[ {}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.003 |
|
|
\[ {}x^{\prime } = -\frac {t}{x} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.038 |
|
|
\[ {}\left (2 u+1\right ) u^{\prime }-t -1 = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.651 |
|
|
\[ {}x^{\prime } = \frac {t^{2}}{1-x^{2}} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
34.553 |
|
|
\[ {}t x^{\prime } = -x+t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.892 |
|
|
\[ {}3 x +2 y+\left (y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.587 |
|
|
\[ {}2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.852 |
|
|
\[ {}2 x y-3+\left (x^{2}+4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.571 |
|
|
\[ {}x +2 y+\left (2 x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.956 |
|
|
\[ {}3 x -y-\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.328 |
|
|
\[ {}x y^{\prime }+\frac {\left (2 x +1\right ) y}{1+x} = -1+x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.237 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.466 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
9.043 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x^{2} \] |
1 |
0 |
0 |
[_linear] |
✗ |
N/A |
1.396 |
|
|
\[ {}x y^{\prime }+y = x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.125 |
|
|
\[ {}y^{\prime } = \frac {x +y-3}{-x +y+1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.433 |
|
|
\[ {}\left (-x +y^{2}\right ) y^{\prime }-y+x^{2} = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
13.914 |
|
|
\[ {}1+y-\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.373 |
|
|
\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.889 |
|
|
\[ {}x y^{\prime }+x +y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.254 |
|
|
\[ {}x^{2}+y+\left (x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.257 |
|
|
\[ {}y-3 x^{2}-\left (4 y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.303 |
|
|
\[ {}\left (y^{3}-x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
2.472 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.197 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +3 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.579 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.806 |
|
|
\[ {}y^{\prime } = \frac {x}{y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
5.332 |
|
|
\[ {}y^{\prime } = \frac {2 x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.724 |
|
|
\[ {}x -y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.227 |
|
|
\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.566 |
|
|
\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.958 |
|
|
\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.991 |
|
|
\[ {}y^{\prime } = -\frac {3 x^{2}}{2 y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.318 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.643 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.719 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.141 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.289 |
|
|
\[ {}y^{\prime } = \frac {t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.332 |
|
|
\[ {}y^{\prime } = \frac {4 t}{1+3 y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
154.546 |
|
|
\[ {}y^{\prime } = \frac {t}{y-2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.28 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.137 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.833 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.886 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.484 |
|
|
\[ {}y^{\prime } = \frac {\left (t +1\right )^{2}}{\left (y+1\right )^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
142.759 |
|
|
\[ {}y y^{\prime } = 2 x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.46 |
|
|
\[ {}\left (y-2\right ) y^{\prime } = x -3 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.321 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.408 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.223 |
|
|
\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
163.516 |
|
|
\[ {}y^{\prime } = \frac {2+\sqrt {x}}{2+\sqrt {y}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
99.218 |
|
|
\[ {}y^{\prime } = \frac {x -y}{x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.326 |
|
|
\[ {}2-2 x +3 y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
12.222 |
|
|
\[ {}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.842 |
|
|
\[ {}x \left (1-2 y\right )+\left (y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.736 |
|
|
\[ {}y^{\prime } = -\frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.871 |
|
|
\[ {}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.77 |
|
|
\[ {}t y^{\prime }+y = t^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.257 |
|
|
\[ {}y^{\prime } = -\frac {t}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
20.007 |
|
|
\[ {}y^{\prime } = \frac {x}{y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
6.905 |
|
|
\[ {}y^{\prime } = \frac {5^{-t}}{y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
50.23 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {t}}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
5.73 |
|
|
\[ {}y^{\prime } = -\frac {y-2}{-2+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.186 |
|
|
\[ {}t y^{\prime }+y = t^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.039 |
|
|
\[ {}t y^{\prime }+y = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.537 |
|
|
\[ {}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.479 |
|
|
\[ {}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.252 |
|
|
\[ {}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.712 |
|
|
\[ {}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}3 t y^{2}+y^{3} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.883 |
|
|
\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.963 |
|
|
\[ {}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
10.187 |
|
|
\[ {}2 t y^{2}+2 t^{2} y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.845 |
|
|
\[ {}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.512 |
|
|
\[ {}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.456 |
|
|
\[ {}t^{2} y+t^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.082 |
|
|
\[ {}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.076 |
|
|
\[ {}\sqrt {t^{2}+1}+y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.096 |
|
|
\[ {}y+\left (t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.825 |
|
|
\[ {}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.86 |
|
|
\[ {}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.359 |
|
|
\[ {}y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
7.595 |
|
|
\[ {}y-t +\left (t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.921 |
|
|
\[ {}t^{2}-y+\left (-t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.964 |
|
|
\[ {}x^{\prime }+\frac {x}{y} = y^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.267 |
|
|
\[ {}2 x -y-2+\left (-x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.896 |
|
|
\[ {}y^{\prime } = \frac {t}{y^{3}} \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
2.13 |
|
|
\[ {}y^{\prime } = -\frac {y}{t -2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.637 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.51 |
|
|
\[ {}y^{\prime } = -\frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.709 |
|
|
\[ {}x y^{\prime } = 2 x -y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.59 |
|
|
\[ {}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.026 |
|
|
\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.454 |
|
|
\[ {}x +y-2+\left (-y+4+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.743 |
|
|
\[ {}x +y+\left (x -y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.56 |
|
|
\[ {}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.665 |
|
|
\[ {}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.536 |
|
|
\[ {}x +y+\left (x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.97 |
|
|
\[ {}x^{2}-x y^{\prime } = y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.849 |
|
|
\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.484 |
|
|
\[ {}x y^{\prime }+y = 2 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.009 |
|
|
\[ {}3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_exact, _rational] |
✓ |
✓ |
22.627 |
|
|
|
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|
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|
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