| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 t y^{2}+y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.138 |
|
| \begin{align*}
t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.668 |
|
| \begin{align*}
\sin \left (2 t \right ) y+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
7.093 |
|
| \begin{align*}
\ln \left (t y\right )+\frac {t y^{\prime }}{y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
✓ |
✓ |
3.976 |
|
| \begin{align*}
{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.166 |
|
| \begin{align*}
3 t^{2}-y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
-1+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.073 |
|
| \begin{align*}
2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.000 |
|
| \begin{align*}
-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
4.204 |
|
| \begin{align*}
2 t y+\left (t^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.648 |
|
| \begin{align*}
2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.387 |
|
| \begin{align*}
\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.587 |
|
| \begin{align*}
3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.849 |
|
| \begin{align*}
{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.414 |
|
| \begin{align*}
3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime }&=0 \\
\end{align*} | [_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] | ✓ | ✓ | ✓ | ✗ | 2.869 |
|
| \begin{align*}
-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.385 |
|
| \begin{align*}
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 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
4.499 |
|
| \begin{align*}
2 t \sin \left (y\right )-2 \sin \left (t^{2}\right ) y t +\left (\cos \left (y\right ) t^{2}+\cos \left (t^{2}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.707 |
|
| \begin{align*}
\left (t +3\right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (t +3\right ) \cos \left (t +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
5.495 |
|
| \begin{align*}
\frac {2 t^{2} y \cos \left (t^{2}\right )-\sin \left (t^{2}\right ) y}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t}&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.071 |
|
| \begin{align*}
-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.421 |
|
| \begin{align*}
2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.555 |
|
| \begin{align*}
2 t y^{2}+2 t^{2} y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \begin{align*}
2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.777 |
|
| \begin{align*}
1+5 t -y-\left (t +2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.973 |
|
| \begin{align*}
{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✗ |
✗ |
✗ |
4.040 |
|
| \begin{align*}
2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
30.435 |
|
| \begin{align*}
y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.393 |
|
| \begin{align*}
\cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
30.786 |
|
| \begin{align*}
\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✓ |
✗ |
✗ |
✗ |
2.478 |
|
| \begin{align*}
\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} | [_exact] | ✓ | ✗ | ✗ | ✗ | 4.932 |
|
| \begin{align*}
-2 x -y \cos \left (y x \right )+\left (2 y-x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
2.777 |
|
| \begin{align*}
-4 x^{3}+6 y \sin \left (6 y x \right )+\left (4 y^{3}+6 x \sin \left (6 y x \right )\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.858 |
|
| \begin{align*}
t^{2} y+t^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.400 |
|
| \begin{align*}
y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.238 |
|
| \begin{align*}
y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| \begin{align*}
2 t y+y^{2}-t^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.480 |
|
| \begin{align*}
y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \begin{align*}
5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
2.405 |
|
| \begin{align*}
5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.579 |
|
| \begin{align*}
2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.914 |
|
| \begin{align*}
2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.165 |
|
| \begin{align*}
-1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.329 |
|
| \begin{align*}
2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.130 |
|
| \begin{align*}
\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.261 |
|
| \begin{align*}
2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.899 |
|
| \begin{align*}
-\frac {y}{2}+y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.932 |
|
| \begin{align*}
y+y^{\prime }&=t y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.236 |
|
| \begin{align*}
2 t y^{\prime }-y&=2 t y^{3} \cos \left (t \right ) \\
\end{align*} | [_Bernoulli] | ✓ | ✓ | ✓ | ✓ | 30.071 |
|
| \begin{align*}
-y+t y^{\prime }&=t y^{3} \sin \left (t \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.561 |
|
| \begin{align*}
-2 y+y^{\prime }&=\frac {\cos \left (t \right )}{\sqrt {y}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.306 |
|
| \begin{align*}
3 y+y^{\prime }&=\sqrt {y}\, \sin \left (t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.145 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.165 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.425 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.254 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t^{2} y^{{3}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.625 |
|
| \begin{align*}
\cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.062 |
|
| \begin{align*}
y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.155 |
|
| \begin{align*}
2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.459 |
|
| \begin{align*}
\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.936 |
|
| \begin{align*}
\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.415 |
|
| \begin{align*}
\sqrt {t^{2}+1}+y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.155 |
|
| \begin{align*}
2 t +\left (y-3 t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.555 |
|
| \begin{align*}
2 y-3 t +t y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.548 |
|
| \begin{align*}
t y-y^{2}+t \left (t -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.921 |
|
| \begin{align*}
t^{2}+t y+y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
10.886 |
|
| \begin{align*}
t^{3}+y^{3}-t y^{2} y^{\prime }&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _Bernoulli] | ✓ | ✓ | ✓ | ✓ | 6.036 |
|
| \begin{align*}
y^{\prime }&=\frac {t +4 y}{4 t +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.013 |
|
| \begin{align*}
t -y+t y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.475 |
|
| \begin{align*}
y+\left (t +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.467 |
|
| \begin{align*}
2 t^{2}-7 t y+5 y^{2}+t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
26.759 |
|
| \begin{align*}
y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.868 |
|
| \begin{align*}
y^{2}&=\left (t y-4 t^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
12.836 |
|
| \begin{align*}
y-\left (3 \sqrt {t y}+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.141 |
|
| \begin{align*}
\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.092 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.782 |
|
| \begin{align*}
t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.224 |
|
| \begin{align*}
y^{\prime }+2 y&=t^{2} \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
2.108 |
|
| \begin{align*}
-2 y+y^{\prime }&=t^{2} \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✗ |
✓ |
✓ |
✗ |
4.826 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}-t^{2}}{2 t y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.684 |
|
| \begin{align*}
t +y-t y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.845 |
|
| \begin{align*}
t y^{\prime }-y-\sqrt {t^{2}+y^{2}}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.320 |
|
| \begin{align*}
t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} | [[_homogeneous, ‘class A‘], _dAlembert] | ✓ | ✓ | ✓ | ✗ | 17.567 |
|
| \begin{align*}
y^{3}-t^{3}-t y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.552 |
|
| \begin{align*}
t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.590 |
|
| \begin{align*}
y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
16.812 |
|
| \begin{align*}
1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.895 |
|
| \begin{align*}
5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.384 |
|
| \begin{align*}
3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.832 |
|
| \begin{align*}
2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.892 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=y^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Bernoulli] |
✗ |
✓ |
✓ |
✗ |
7.084 |
|
| \begin{align*}
t y^{\prime }-{y^{\prime }}^{3}&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.432 |
|
| \begin{align*}
t y^{\prime }-y-2 \left (-y+t y^{\prime }\right )^{2}&=y^{\prime }+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.464 |
|
| \begin{align*}
t y^{\prime }-y-1&={y^{\prime }}^{2}-y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|