| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 t y^{2}+y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.687 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.611 |
|
| \begin{align*}
\ln \left (t y\right )+\frac {t y^{\prime }}{y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
✓ |
✓ |
5.371 |
|
| \begin{align*}
{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.138 |
|
| \begin{align*}
3 t^{2}-y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
-1+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.141 |
|
| \begin{align*}
2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.540 |
|
| \begin{align*}
-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
14.136 |
|
| \begin{align*}
2 t y+\left (t^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
300.106 |
|
| \begin{align*}
2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
55.974 |
|
| \begin{align*}
\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.093 |
|
| \begin{align*}
3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.523 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
2.598 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
4.275 |
|
| \begin{align*}
-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
4.032 |
|
| \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’)‘] |
✗ |
✗ |
✗ |
✗ |
30.526 |
|
| \begin{align*}
2 t \sin \left (y\right )-2 y \sin \left (t^{2}\right ) t +\left (\cos \left (y\right ) t^{2}+\cos \left (t^{2}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.079 |
|
| \begin{align*}
\left (t +3\right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (t +3\right ) \cos \left (y+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
6.749 |
|
| \begin{align*}
\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{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‘]] |
✓ |
✓ |
✓ |
✗ |
6.832 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
12.793 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
13.282 |
|
| \begin{align*}
2 t y^{2}+2 t^{2} y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \begin{align*}
2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
10.138 |
|
| \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] |
✓ |
✓ |
✗ |
✗ |
6.704 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
26.543 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
0.559 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
28.381 |
|
| \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] |
✗ |
✗ |
✗ |
✗ |
176.700 |
|
| \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] |
✓ |
✓ |
✗ |
✗ |
3.460 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
3.181 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
4.740 |
|
| \begin{align*}
t^{2} y+t^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.985 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
3.583 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
2.060 |
|
| \begin{align*}
2 t y+y^{2}-t^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.142 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
3.428 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
4.375 |
|
| \begin{align*}
5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.799 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.435 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
3.984 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
3.658 |
|
| \begin{align*}
2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
60.895 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
39.595 |
|
| \begin{align*}
-\frac {y}{2}+y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.473 |
|
| \begin{align*}
y+y^{\prime }&=t y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.520 |
|
| \begin{align*}
2 y^{\prime } t -y&=2 t y^{3} \cos \left (t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.688 |
|
| \begin{align*}
-y+y^{\prime } t&=t y^{3} \sin \left (t \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.764 |
|
| \begin{align*}
-2 y+y^{\prime }&=\frac {\cos \left (t \right )}{\sqrt {y}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.759 |
|
| \begin{align*}
3 y+y^{\prime }&=\sqrt {y}\, \sin \left (t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.878 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.261 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.394 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.846 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t^{2} y^{{3}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
114.626 |
|
| \begin{align*}
\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.872 |
|
| \begin{align*}
y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.491 |
|
| \begin{align*}
2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.108 |
|
| \begin{align*}
\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.334 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
14.875 |
|
| \begin{align*}
\sqrt {t^{2}+1}+y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
2 t +\left (y-3 t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.659 |
|
| \begin{align*}
2 y-3 t +y^{\prime } t&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.350 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
21.076 |
|
| \begin{align*}
t^{2}+t y+y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
25.853 |
|
| \begin{align*}
t^{3}+y^{3}-t y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.105 |
|
| \begin{align*}
y^{\prime }&=\frac {t +4 y}{4 t +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.322 |
|
| \begin{align*}
t -y+y^{\prime } t&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.553 |
|
| \begin{align*}
y+\left (y+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.323 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
55.447 |
|
| \begin{align*}
y+2 \sqrt {t^{2}+y^{2}}-y^{\prime } t&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.050 |
|
| \begin{align*}
y^{2}&=\left (t y-4 t^{2}\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
14.675 |
|
| \begin{align*}
y-\left (3 \sqrt {t y}+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.730 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.395 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.013 |
|
| \begin{align*}
t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.270 |
|
| \begin{align*}
y^{\prime }+2 y&=t^{2} \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
2.421 |
|
| \begin{align*}
-2 y+y^{\prime }&=t^{2} \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
2.424 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
10.127 |
|
| \begin{align*}
t +y-y^{\prime } t&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.757 |
|
| \begin{align*}
y^{\prime } t -y-\sqrt {t^{2}+y^{2}}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.689 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
14.474 |
|
| \begin{align*}
y^{3}-t^{3}-t y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.054 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
18.926 |
|
| \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] |
✓ |
✓ |
✗ |
✓ |
12.062 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
26.831 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.641 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
9.644 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
8.053 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.238 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=y^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
82.036 |
|
| \begin{align*}
y^{\prime } t -{y^{\prime }}^{3}&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.605 |
|
| \begin{align*}
y^{\prime } t -y-2 \left (-y+y^{\prime } t \right )^{2}&=y^{\prime }+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.891 |
|
| \begin{align*}
y^{\prime } t -y-1&={y^{\prime }}^{2}-y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|