| # | ID | ODE | CAS classification |
Maple |
Mma |
Sympy |
time(sec) |
| \(1\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
5.562 |
|
| \(2\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2}-1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✗ |
24.157 |
|
| \(3\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
6.963 |
|
| \(4\) |
\begin{align*}
y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.896 |
|
| \(5\) |
\begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.490 |
|
| \(6\) |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
10.588 |
|
| \(7\) |
\begin{align*}
x \ln \left (x \right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
35.975 |
|
| \(8\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{\sin \left (x \right )} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
10.056 |
|
| \(9\) |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}+y}{x^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
3.222 |
|
| \(10\) |
\begin{align*}
y^{\prime }&=\tan \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
1.477 |
|
| \(11\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{\ln \left (y x \right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.838 |
|
| \(12\) |
\begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right ) y^{{1}/{3}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.652 |
|
| \(13\) |
\begin{align*}
y^{\prime }&=\ln \left (1+x^{2}+y^{2}\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.773 |
|
| \(14\) |
\begin{align*}
y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
4.503 |
|
| \(15\) |
\begin{align*}
y^{\prime }&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.139 |
|
| \(16\) |
\begin{align*}
2 x^{2}+8 y x +y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
3.635 |
|
| \(17\) |
\begin{align*}
y \sin \left (y x \right )+x y^{2} \cos \left (y x \right )+\left (x \sin \left (y x \right )+x y^{2} \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.529 |
|
| \(18\) |
\begin{align*}
y^{\prime }&=y^{2}+\cos \left (t^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
29.585 |
|
| \(19\) |
\begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
19.703 |
|
| \(20\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
29.458 |
|
| \(21\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
25.289 |
|
| \(22\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
26.019 |
|
| \(23\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.399 |
|
| \(24\) |
\begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
1.128 |
|
| \(25\) |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.668 |
|
| \(26\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.707 |
|
| \(27\) |
\begin{align*}
2 t \cos \left (y\right )+3 t^{2} y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
38.915 |
|
| \(28\) |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
6.707 |
|
| \(29\) |
\begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
15.663 |
|
| \(30\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
25.375 |
|
| \(31\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
25.471 |
|
| \(32\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t^{2}}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
25.678 |
|
| \(33\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
0.904 |
|
| \(34\) |
\begin{align*}
y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \\
y \left (0\right ) &= {\frac {2}{5}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
0.853 |
|
| \(35\) |
\begin{align*}
y^{\prime }&=\left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.121 |
|
| \(36\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-t}+\ln \left (1+y^{2}\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.072 |
|
| \(37\) |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{-y}+2 t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.428 |
|
| \(38\) |
\begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{1+t +y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
1.349 |
|
| \(39\) |
\begin{align*}
x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
26.365 |
|
| \(40\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=x \left (-x^{2}+1\right ) \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✗ |
4.994 |
|
| \(41\) |
\begin{align*}
1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
17.984 |
|
| \(42\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (y x -1\right ) y^{\prime }&=y \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
65.586 |
|
| \(43\) |
\begin{align*}
y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2}&=r \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
12.489 |
|
| \(44\) |
\begin{align*}
y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
4.569 |
|
| \(45\) |
\begin{align*}
y^{2} \left (x^{2}+1\right )+y+\left (2 y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
8.263 |
|
| \(46\) |
\begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
12.937 |
|
| \(47\) |
\begin{align*}
x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
1.582 |
|
| \(48\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+a y+b y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
2.108 |
|
| \(49\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+a y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
3.234 |
|
| \(50\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
7.996 |
|
| \(51\) |
\begin{align*}
y^{\prime }+\left (a x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
3.471 |
|
| \(52\) |
\begin{align*}
y^{\prime }&=\left (a \,{\mathrm e}^{x}+y\right ) y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
3.970 |
|
| \(53\) |
\begin{align*}
y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
3.700 |
|
| \(54\) |
\begin{align*}
y^{\prime }&=f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
1.664 |
|
| \(55\) |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
7.564 |
|
| \(56\) |
\begin{align*}
y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
6.018 |
|
| \(57\) |
\begin{align*}
y^{\prime }&=x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
5.967 |
|
| \(58\) |
\begin{align*}
2 y^{\prime }&=2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
52.014 |
|
| \(59\) |
\begin{align*}
y^{\prime } x&=\sin \left (x -y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
283.430 |
|
| \(60\) |
\begin{align*}
y^{\prime } x +n y&=f \left (x \right ) g \left (x^{n} y\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
4.730 |
|
| \(61\) |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}-a y^{3} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
2.392 |
|
| \(62\) |
\begin{align*}
x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
3.280 |
|
| \(63\) |
\begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
15.930 |
|
| \(64\) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=n \left (1-2 y x +y^{2}\right ) \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
2.269 |
|
| \(65\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2}-2 x y \left (1+y^{2}\right ) \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
54.878 |
|
| \(66\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )&=x \left (x^{2}+1\right ) \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
22.958 |
|
| \(67\) |
\begin{align*}
\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
14.895 |
|
| \(68\) |
\begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
32.012 |
|
| \(69\) |
\begin{align*}
x^{k} y^{\prime }&=a \,x^{m}+b y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
2.271 |
|
| \(70\) |
\begin{align*}
y y^{\prime }+x^{3}+y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
4.577 |
|
| \(71\) |
\begin{align*}
y y^{\prime }+f \left (x \right )&=g \left (x \right ) y \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
5.449 |
|
| \(72\) |
\begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
8.921 |
|
| \(73\) |
\begin{align*}
\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
27.361 |
|
| \(74\) |
\begin{align*}
x \left (a +y\right ) y^{\prime }+b x +c y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
12.268 |
|
| \(75\) |
\begin{align*}
\left (a +x \left (x +y\right )\right ) y^{\prime }&=b \left (x +y\right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
22.207 |
|
| \(76\) |
\begin{align*}
\left (1-x^{2} y\right ) y^{\prime }-1+x y^{2}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
55.832 |
|
| \(77\) |
\begin{align*}
x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
26.688 |
|
| \(78\) |
\begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
4.411 |
|
| \(79\) |
\begin{align*}
\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime }&=y^{3} \csc \left (x \right ) \sec \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✗ |
31.545 |
|
| \(80\) |
\begin{align*}
\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
4.192 |
|
| \(81\) |
\begin{align*}
f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✗ |
7.505 |
|
| \(82\) |
\begin{align*}
{y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
14.239 |
|
| \(83\) |
\begin{align*}
x^{2} {y^{\prime }}^{2}+x \left (x^{2}+y x -2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
64.336 |
|
| \(84\) |
\begin{align*}
x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
22.019 |
|
| \(85\) |
\begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
172.437 |
|
| \(86\) |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
334.747 |
|
| \(87\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
10.872 |
|
| \(88\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
16.401 |
|
| \(89\) |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
14.062 |
|
| \(90\) |
\begin{align*}
x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right )&=a^{2} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
0.797 |
|
| \(91\) |
\begin{align*}
\left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime }&=y-x^{2} \sqrt {x^{2}-y^{2}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
31.998 |
|
| \(92\) |
\begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
10.603 |
|
| \(93\) |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
11.670 |
|
| \(94\) |
\begin{align*}
\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
17.043 |
|
| \(95\) |
\begin{align*}
s^{\prime }&=t \ln \left (s^{2 t}\right )+8 t^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
9.990 |
|
| \(96\) |
\begin{align*}
s^{2}+s^{\prime }&=\frac {s+1}{s t} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
27.762 |
|
| \(97\) |
\begin{align*}
x^{\prime }+t x&={\mathrm e}^{x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
8.686 |
|
| \(98\) |
\begin{align*}
x x^{\prime }+t^{2} x&=\sin \left (t \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
70.901 |
|
| \(99\) |
\begin{align*}
5 x^{2} y+6 x^{3} y^{2}+4 x y^{2}+\left (2 x^{3}+3 x^{4} y+3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
24.019 |
|
| \(100\) |
\begin{align*}
2 x +2 y+2 x^{3} y+4 y^{2} x^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
18.353 |
|
| \(101\) |
\begin{align*}
1+\frac {1}{1+x^{2}+4 y x +y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 y x +y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
51.012 |
|
| \(102\) |
\begin{align*}
\sqrt {\frac {y}{x}}+\cos \left (x \right )+\left (\sqrt {\frac {x}{y}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
58.102 |
|
| \(103\) |
\begin{align*}
\sin \left (x^{\prime }\right )+y^{3} x&=\sin \left (y \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
26.093 |
|
| \(104\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
14.722 |
|
| \(105\) |
\begin{align*}
y^{\prime }&=6 \sqrt {y}+5 x^{3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
4.232 |
|
| \(106\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
10.366 |
|
| \(107\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
2.763 |
|
| \(108\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.136 |
|
| \(109\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.149 |
|
| \(110\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
1.144 |
|
| \(111\) |
\begin{align*}
y^{\prime } x -4 y&=x^{6} {\mathrm e}^{x} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_linear] |
✗ |
✗ |
✗ |
3.656 |
|
| \(112\) |
\begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✗ |
✗ |
✓ |
1.062 |
|
| \(113\) |
\begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
13.515 |
|
| \(114\) |
\begin{align*}
y^{\prime }&=y+x \,{\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.951 |
|
| \(115\) |
\begin{align*}
y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
4.147 |
|
| \(116\) |
\begin{align*}
{y^{\prime }}^{2}+y^{2}&=\sec \left (x \right )^{4} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
64.119 |
|
| \(117\) |
\begin{align*}
y^{\prime }&=\frac {y x +3 x -2 y+6}{y x -3 x -2 y+6} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
16.251 |
|
| \(118\) |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y^{2}}{x} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
6.982 |
|
| \(119\) |
\begin{align*}
y^{\prime }-\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}+\frac {g^{\prime }\left (x \right )}{f \left (x \right )}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
6.645 |
|
| \(120\) |
\begin{align*}
y^{\prime }+y^{3}+a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
7.977 |
|
| \(121\) |
\begin{align*}
y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
5.476 |
|
| \(122\) |
\begin{align*}
y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
7.868 |
|
| \(123\) |
\begin{align*}
y^{\prime }-x \left (2+x \right ) y^{3}-\left (x +3\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
8.047 |
|
| \(124\) |
\begin{align*}
y^{\prime }+\left (4 a^{2} x +3 a \,x^{2}+b \right ) y^{3}+3 x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
15.330 |
|
| \(125\) |
\begin{align*}
y^{\prime }+2 \left (a^{2} x^{3}-b^{2} x \right ) y^{3}+3 b y^{2}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
10.658 |
|
| \(126\) |
\begin{align*}
y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
38.175 |
|
| \(127\) |
\begin{align*}
y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
39.437 |
|
| \(128\) |
\begin{align*}
y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right )&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
7.446 |
|
| \(129\) |
\begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
11.127 |
|
| \(130\) |
\begin{align*}
y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
4.550 |
|
| \(131\) |
\begin{align*}
y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
4.194 |
|
| \(132\) |
\begin{align*}
y^{\prime }-\frac {y-x^{2} \sqrt {x^{2}-y^{2}}}{x y \sqrt {x^{2}-y^{2}}+x}&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
32.516 |
|
| \(133\) |
\begin{align*}
y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
11.658 |
|
| \(134\) |
\begin{align*}
y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
5.456 |
|
| \(135\) |
\begin{align*}
y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
3.117 |
|
| \(136\) |
\begin{align*}
y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
3.469 |
|
| \(137\) |
\begin{align*}
y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.432 |
|
| \(138\) |
\begin{align*}
y^{\prime }-\tan \left (y x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
1.080 |
|
| \(139\) |
\begin{align*}
y^{\prime }-x^{a -1} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
11.213 |
|
| \(140\) |
\begin{align*}
2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
36.308 |
|
| \(141\) |
\begin{align*}
y^{\prime } x +y^{3}+3 x y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
11.253 |
|
| \(142\) |
\begin{align*}
y^{\prime } x -\sin \left (x -y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
265.181 |
|
| \(143\) |
\begin{align*}
y^{\prime } x +a y-f \left (x \right ) g \left (x^{a} y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
6.262 |
|
| \(144\) |
\begin{align*}
x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
5.470 |
|
| \(145\) |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
9.884 |
|
| \(146\) |
\begin{align*}
x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
8.028 |
|
| \(147\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
58.483 |
|
| \(148\) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
17.802 |
|
| \(149\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a \left (1-2 y x +y^{2}\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
5.705 |
|
| \(150\) |
\begin{align*}
\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
11.745 |
|
| \(151\) |
\begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
26.684 |
|
| \(152\) |
\begin{align*}
y y^{\prime }+x^{3}+y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
12.817 |
|
| \(153\) |
\begin{align*}
y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
100.919 |
|
| \(154\) |
\begin{align*}
y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
25.267 |
|
| \(155\) |
\begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
11.035 |
|
| \(156\) |
\begin{align*}
y y^{\prime } x -y^{2}+y x +x^{3}-2 x^{2}&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
37.591 |
|
| \(157\) |
\begin{align*}
x \left (a +y\right ) y^{\prime }+b y+c x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
19.952 |
|
| \(158\) |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
64.987 |
|
| \(159\) |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
80.703 |
|
| \(160\) |
\begin{align*}
x \left (y x +x^{4}-1\right ) y^{\prime }-y \left (y x -x^{4}-1\right )&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
28.517 |
|
| \(161\) |
\begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
4.879 |
|
| \(162\) |
\begin{align*}
\left (2 a y^{3}+3 a x y^{2}-b \,x^{3}+c \,x^{2}\right ) y^{\prime }-a y^{3}+c y^{2}+3 b \,x^{2} y+2 b \,x^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
8.601 |
|
| \(163\) |
\begin{align*}
y^{\prime } \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
34.771 |
|
| \(164\) |
\begin{align*}
y^{\prime } \cos \left (y\right )+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
55.100 |
|
| \(165\) |
\begin{align*}
x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
39.910 |
|
| \(166\) |
\begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
67.707 |
|
| \(167\) |
\begin{align*}
x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
38.771 |
|
| \(168\) |
\begin{align*}
\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
69.818 |
|
| \(169\) |
\begin{align*}
\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
15.169 |
|
| \(170\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
68.736 |
|
| \(171\) |
\begin{align*}
\left (a y^{2}+b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
185.527 |
|
| \(172\) |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
199.212 |
|
| \(173\) |
\begin{align*}
x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (-x +y\right ) y^{\prime }-y^{2} \left (x^{2} y-1\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
40.130 |
|
| \(174\) |
\begin{align*}
\left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
39.216 |
|
| \(175\) |
\begin{align*}
x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (y^{2} x^{4}-1\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
26.787 |
|
| \(176\) |
\begin{align*}
\left (a^{2} \sqrt {x^{2}+y^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +a^{2} \sqrt {x^{2}+y^{2}}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
101.197 |
|
| \(177\) |
\begin{align*}
\left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
141.386 |
|
| \(178\) |
\begin{align*}
f \left (x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
40.511 |
|
| \(179\) |
\begin{align*}
{y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
86.060 |
|
| \(180\) |
\begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
319.104 |
|
| \(181\) |
\begin{align*}
x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
9.614 |
|
| \(182\) |
\begin{align*}
y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
0.225 |
|
| \(183\) |
\begin{align*}
f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
51.729 |
|
| \(184\) |
\begin{align*}
a \,x^{n} f \left (y^{\prime }\right )+y^{\prime } x -y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
3.437 |
|
| \(185\) |
\begin{align*}
f \left (x {y^{\prime }}^{2}\right )+2 y^{\prime } x -y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
1.227 |
|
| \(186\) |
\begin{align*}
f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
4.955 |
|
| \(187\) |
\begin{align*}
y^{\prime }&=\frac {1+2 F \left (\frac {4 x^{2} y+1}{4 x^{2}}\right ) x}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
5.065 |
|
| \(188\) |
\begin{align*}
y^{\prime }&=\frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
5.155 |
|
| \(189\) |
\begin{align*}
y^{\prime }&=F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
9.100 |
|
| \(190\) |
\begin{align*}
y^{\prime }&=\frac {\left (x^{{3}/{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
6.719 |
|
| \(191\) |
\begin{align*}
y^{\prime }&=\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
7.433 |
|
| \(192\) |
\begin{align*}
y^{\prime }&=\frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
7.411 |
|
| \(193\) |
\begin{align*}
y^{\prime }&=\frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
18.187 |
|
| \(194\) |
\begin{align*}
y^{\prime }&=\frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
5.956 |
|
| \(195\) |
\begin{align*}
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} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
5.509 |
|
| \(196\) |
\begin{align*}
y^{\prime }&=\frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
5.090 |
|
| \(197\) |
\begin{align*}
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 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
10.970 |
|
| \(198\) |
\begin{align*}
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} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
16.266 |
|
| \(199\) |
\begin{align*}
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} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
45.155 |
|
| \(200\) |
\begin{align*}
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 )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
5.996 |
|
| \(201\) |
\begin{align*}
y^{\prime }&=\frac {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
1.701 |
|
| \(202\) |
\begin{align*}
y^{\prime }&=\frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
12.784 |
|
| \(203\) |
\begin{align*}
y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
7.346 |
|
| \(204\) |
\begin{align*}
y^{\prime }&=\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
9.155 |
|
| \(205\) |
\begin{align*}
y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
11.419 |
|
| \(206\) |
\begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
12.399 |
|
| \(207\) |
\begin{align*}
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 )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
26.300 |
|
| \(208\) |
\begin{align*}
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 )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
2.004 |
|
| \(209\) |
\begin{align*}
y^{\prime }&=\frac {\left (-2 y^{{3}/{2}}+3 \,{\mathrm e}^{x}\right )^{2} {\mathrm e}^{x}}{4 \sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
9.894 |
|
| \(210\) |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
205.534 |
|
| \(211\) |
\begin{align*}
y^{\prime }&=\frac {x +1+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
12.211 |
|
| \(212\) |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
23.738 |
|
| \(213\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
13.929 |
|
| \(214\) |
\begin{align*}
y^{\prime }&=\frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
12.176 |
|
| \(215\) |
\begin{align*}
y^{\prime }&=\frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 x +3} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
21.216 |
|
| \(216\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
48.864 |
|
| \(217\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right )^{2} x \left (1+y\right )^{2}}{16} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
57.543 |
|
| \(218\) |
\begin{align*}
y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
53.760 |
|
| \(219\) |
\begin{align*}
y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
18.617 |
|
| \(220\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
14.441 |
|
| \(221\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
15.227 |
|
| \(222\) |
\begin{align*}
y^{\prime }&=\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
108.700 |
|
| \(223\) |
\begin{align*}
y^{\prime }&=\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
201.241 |
|
| \(224\) |
\begin{align*}
y^{\prime }&=\frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
15.384 |
|
| \(225\) |
\begin{align*}
y^{\prime }&=\frac {-x^{2}-x -a x -a +2 x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
16.314 |
|
| \(226\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
8.374 |
|
| \(227\) |
\begin{align*}
y^{\prime }&=-\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
69.358 |
|
| \(228\) |
\begin{align*}
y^{\prime }&=\frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
40.633 |
|
| \(229\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
9.173 |
|
| \(230\) |
\begin{align*}
y^{\prime }&=\frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✗ |
8.939 |
|
| \(231\) |
\begin{align*}
y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
29.979 |
|
| \(232\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
9.084 |
|
| \(233\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
27.480 |
|
| \(234\) |
\begin{align*}
y^{\prime }&=-\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
5.248 |
|
| \(235\) |
\begin{align*}
y^{\prime }&=\frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
9.735 |
|
| \(236\) |
\begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{4}+x^{4}}{2 x \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
11.933 |
|
| \(237\) |
\begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+x \cos \left (2 y\right )+x}{2 x \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
72.722 |
|
| \(238\) |
\begin{align*}
y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
6.263 |
|
| \(239\) |
\begin{align*}
y^{\prime }&=\frac {x^{3} {\mathrm e}^{y}+x^{4}+{\mathrm e}^{y} y-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+y x -\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
33.670 |
|
| \(240\) |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
21.117 |
|
| \(241\) |
\begin{align*}
y^{\prime }&=\frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
18.908 |
|
| \(242\) |
\begin{align*}
y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{3} \cos \left (2 y\right ) \ln \left (x \right )+x^{3} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
11.025 |
|
| \(243\) |
\begin{align*}
y^{\prime }&=-\frac {2 x}{3}+\sqrt {x^{2}+3 y}+x^{2} \sqrt {x^{2}+3 y}+x^{3} \sqrt {x^{2}+3 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
14.375 |
|
| \(244\) |
\begin{align*}
y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{2} \cos \left (2 y\right ) \ln \left (x \right )+\ln \left (x \right ) x^{2}}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
10.973 |
|
| \(245\) |
\begin{align*}
y^{\prime }&=\frac {\left (3 x y^{2}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
17.595 |
|
| \(246\) |
\begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{3}+2 x^{5} \sqrt {4 x^{2} y+1}+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
13.617 |
|
| \(247\) |
\begin{align*}
y^{\prime }&=\frac {2 a +\sqrt {-y^{2}+4 a x}+x^{2} \sqrt {-y^{2}+4 a x}+x^{3} \sqrt {-y^{2}+4 a x}}{y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
38.025 |
|
| \(248\) |
\begin{align*}
y^{\prime }&=\frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
7.476 |
|
| \(249\) |
\begin{align*}
y^{\prime }&=-\frac {1}{-\left (y^{3}\right )^{{2}/{3}} x -\textit {\_F1} \left (y^{3}-3 \ln \left (x \right )\right ) \left (y^{3}\right )^{{1}/{3}} x} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
6.241 |
|
| \(250\) |
\begin{align*}
y^{\prime }&=\frac {3 x^{3}+\sqrt {-9 x^{4}+4 y^{3}}+x^{2} \sqrt {-9 x^{4}+4 y^{3}}+x^{3} \sqrt {-9 x^{4}+4 y^{3}}}{y^{2}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
46.744 |
|
| \(251\) |
\begin{align*}
y^{\prime }&=\frac {1}{-x +\left (\frac {1}{y}+1\right ) x +\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2}-\textit {\_F1} \left (\left (\frac {1}{y}+1\right ) x \right ) x^{2} \left (\frac {1}{y}+1\right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
5.873 |
|
| \(252\) |
\begin{align*}
y^{\prime }&=\frac {x}{2}+\frac {1}{2}+\sqrt {x^{2}+2 x +1-4 y}+x^{2} \sqrt {x^{2}+2 x +1-4 y}+x^{3} \sqrt {x^{2}+2 x +1-4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
14.630 |
|
| \(253\) |
\begin{align*}
y^{\prime }&=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
8.234 |
|
| \(254\) |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
16.194 |
|
| \(255\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (\cos \left (x \right )+1\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
11.066 |
|
| \(256\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+\ln \left (x \right )^{2} x^{2}+2 x^{2} \ln \left (y\right ) \ln \left (x \right )+x^{2} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
11.990 |
|
| \(257\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y\right )-1+\ln \left (x \right )+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
10.889 |
|
| \(258\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
7.528 |
|
| \(259\) |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+\sqrt {x^{2}-2 x +1+8 y}+x^{2} \sqrt {x^{2}-2 x +1+8 y}+x^{3} \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
14.558 |
|
| \(260\) |
\begin{align*}
y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
7.535 |
|
| \(261\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
6.522 |
|
| \(262\) |
\begin{align*}
y^{\prime }&=\left (\frac {\ln \left (-1+y\right ) y}{\left (1-y\right ) \ln \left (x \right ) x}-\frac {\ln \left (-1+y\right )}{\left (1-y\right ) \ln \left (x \right ) x}-f \left (x \right )\right ) \left (1-y\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
10.357 |
|
| \(263\) |
\begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+\sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✗ |
18.315 |
|
| \(264\) |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x +x^{3}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
8.493 |
|
| \(265\) |
\begin{align*}
y^{\prime }&=-\frac {i \left (32 i x +64+64 y^{4}+32 y^{2} x^{2}+4 x^{4}+64 y^{6}+48 x^{2} y^{4}+12 y^{2} x^{4}+x^{6}\right )}{128 y} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
10.039 |
|
| \(266\) |
\begin{align*}
y^{\prime }&=-\frac {\left (-8-8 y^{3}+24 y^{{3}/{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{{9}/{2}}+36 \,{\mathrm e}^{x} y^{3}-54 \,{\mathrm e}^{2 x} y^{{3}/{2}}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✗ |
37.335 |
|
| \(267\) |
\begin{align*}
y^{\prime }&=-\frac {i \left (i x +1+x^{4}+2 y^{2} x^{2}+y^{4}+x^{6}+3 y^{2} x^{4}+3 x^{2} y^{4}+y^{6}\right )}{y} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
9.460 |
|
| \(268\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (y\right ) x +\ln \left (y\right )-x -1+x \ln \left (x \right )+\ln \left (x \right )+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x \left (x +1\right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
12.510 |
|
| \(269\) |
\begin{align*}
y^{\prime }&=\frac {y \left (x \ln \left (x \right )+\ln \left (x \right )+\ln \left (y\right ) x +\ln \left (y\right )-x -1+\ln \left (x \right )^{2} x +2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}\right )}{x \left (x +1\right )} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
13.934 |
|
| \(270\) |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x \right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
10.092 |
|
| \(271\) |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+{\mathrm e}^{-\frac {y}{x}} x +x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
8.689 |
|
| \(272\) |
\begin{align*}
y^{\prime }&=\frac {y \left (\ln \left (x \right )+\ln \left (y\right )-1+\ln \left (x \right )^{2} x +2 x \ln \left (y\right ) \ln \left (x \right )+x \ln \left (y\right )^{2}+x^{3} \ln \left (x \right )^{2}+2 x^{3} \ln \left (y\right ) \ln \left (x \right )+x^{3} \ln \left (y\right )^{2}+x^{4} \ln \left (x \right )^{2}+2 x^{4} \ln \left (y\right ) \ln \left (x \right )+x^{4} \ln \left (y\right )^{2}\right )}{x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✗ |
12.086 |
|
| \(273\) |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2}-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y+2 x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
24.256 |
|
| \(274\) |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}}-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y+2 x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
22.499 |
|
| \(275\) |
\begin{align*}
y^{\prime }&=\frac {y \left (y^{2} x^{2}+y x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x} \left (-1+x \right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel] |
✓ |
✓ |
✗ |
19.623 |
|
| \(276\) |
\begin{align*}
x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{2}+b x \right ) y+\alpha \,x^{2}+\beta x +\gamma \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
142.235 |
|
| \(277\) |
\begin{align*}
x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
136.812 |
|
| \(278\) |
\begin{align*}
x^{2} y^{\prime }&=\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
151.726 |
|
| \(279\) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+\lambda \left (1-2 y x +y^{2}\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
10.065 |
|
| \(280\) |
\begin{align*}
\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma &=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
552.357 |
|
| \(281\) |
\begin{align*}
x^{3} y^{\prime }&=a \,x^{3} y^{2}+x \left (b x +c \right ) y+x \alpha +\beta \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✗ |
129.691 |
|
| \(282\) |
\begin{align*}
y^{\prime }&=\sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
47.694 |
|
| \(283\) |
\begin{align*}
y^{\prime }&=y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
135.160 |
|
| \(284\) |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\mu x} y^{2}+a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y-b \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
133.017 |
|
| \(285\) |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
45.203 |
|
| \(286\) |
\begin{align*}
y^{\prime }&=a \cosh \left (\lambda x \right ) y^{2}+b \cosh \left (\lambda x \right ) \sinh \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
147.332 |
|
| \(287\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
36.894 |
|
| \(288\) |
\begin{align*}
y^{\prime }&=y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
131.520 |
|
| \(289\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
37.337 |
|
| \(290\) |
\begin{align*}
y^{\prime }&=y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
68.757 |
|
| \(291\) |
\begin{align*}
2 y^{\prime }&=\left (\lambda +a -a \sin \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \sin \left (\lambda x \right ) \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
211.539 |
|
| \(292\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
19.966 |
|
| \(293\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
136.383 |
|
| \(294\) |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
19.488 |
|
| \(295\) |
\begin{align*}
y^{\prime }&=y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
90.375 |
|
| \(296\) |
\begin{align*}
y^{\prime }&=y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
214.642 |
|
| \(297\) |
\begin{align*}
y^{\prime }&=a \cos \left (\lambda x \right ) y^{2}+b \cos \left (\lambda x \right ) \sin \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
157.518 |
|
| \(298\) |
\begin{align*}
y^{\prime }&=y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \\
\end{align*} |
[_Riccati] |
✓ |
✗ |
✗ |
156.374 |
|
| \(299\) |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
50.322 |
|
| \(300\) |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
64.366 |
|
| \(301\) |
\begin{align*}
y^{\prime }&=\lambda \arctan \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
54.357 |
|
| \(302\) |
\begin{align*}
y^{\prime }&=\lambda \operatorname {arccot}\left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
84.839 |
|
| \(303\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tanh \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
84.576 |
|
| \(304\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
83.254 |
|
| \(305\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
34.169 |
|
| \(306\) |
\begin{align*}
y^{\prime } x&=f \left (x \right ) y^{2}+a -a^{2} f \left (x \right ) \ln \left (x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
20.695 |
|
| \(307\) |
\begin{align*}
y^{\prime } x&=f \left (x \right ) \left (y+a \ln \left (x \right )\right )^{2}-a \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✗ |
20.965 |
|
| \(308\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
26.001 |
|
| \(309\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
36.509 |
|
| \(310\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \cos \left (\lambda x \right )+a^{2} f \left (x \right ) \cos \left (\lambda x \right )^{2} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
37.759 |
|
| \(311\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
84.857 |
|
| \(312\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a \cot \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
92.810 |
|
| \(313\) |
\begin{align*}
y^{\prime }&=\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}-\frac {g^{\prime }\left (x \right )}{f \left (x \right )} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
12.161 |
|
| \(314\) |
\begin{align*}
f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right )&=0 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
23.850 |
|
| \(315\) |
\begin{align*}
y^{\prime }&=y^{2}+a^{2} f \left (a x +b \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
8.120 |
|
| \(316\) |
\begin{align*}
y^{\prime }&=y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
9.897 |
|
| \(317\) |
\begin{align*}
x^{2} y^{\prime }&=x^{4} f \left (x \right ) y^{2}+1 \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
12.751 |
|
| \(318\) |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{4}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
68.437 |
|
| \(319\) |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+h \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
15.967 |
|
| \(320\) |
\begin{align*}
x^{2} y^{\prime }&=y^{2} x^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4} \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
20.628 |
|
| \(321\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
195.842 |
|
| \(322\) |
\begin{align*}
y y^{\prime }-y&=2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
120.283 |
|
| \(323\) |
\begin{align*}
y y^{\prime }-y&=A x +\frac {B}{x}-\frac {B^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
61.529 |
|
| \(324\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
52.861 |
|
| \(325\) |
\begin{align*}
y y^{\prime }-y&=A +B \,{\mathrm e}^{-\frac {2 x}{A}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
55.694 |
|
| \(326\) |
\begin{align*}
y y^{\prime }-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
66.385 |
|
| \(327\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
142.803 |
|
| \(328\) |
\begin{align*}
y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
79.763 |
|
| \(329\) |
\begin{align*}
y y^{\prime }-y&=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
90.083 |
|
| \(330\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
126.910 |
|
| \(331\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
129.450 |
|
| \(332\) |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
193.089 |
|
| \(333\) |
\begin{align*}
y y^{\prime }-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
124.206 |
|
| \(334\) |
\begin{align*}
y y^{\prime }-y&=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
175.009 |
|
| \(335\) |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
128.810 |
|
| \(336\) |
\begin{align*}
y y^{\prime }-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
136.084 |
|
| \(337\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
200.927 |
|
| \(338\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
199.850 |
|
| \(339\) |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
112.157 |
|
| \(340\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
178.807 |
|
| \(341\) |
\begin{align*}
y y^{\prime }-y&=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
202.928 |
|
| \(342\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
124.016 |
|
| \(343\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
193.842 |
|
| \(344\) |
\begin{align*}
y y^{\prime }-y&=\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
119.490 |
|
| \(345\) |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
292.074 |
|
| \(346\) |
\begin{align*}
y y^{\prime }-y&=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
236.406 |
|
| \(347\) |
\begin{align*}
y y^{\prime }-y&=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
167.948 |
|
| \(348\) |
\begin{align*}
y y^{\prime }-y&=2 A^{2}-A \sqrt {x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
124.417 |
|
| \(349\) |
\begin{align*}
y y^{\prime }-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
179.365 |
|
| \(350\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
193.366 |
|
| \(351\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
132.089 |
|
| \(352\) |
\begin{align*}
y y^{\prime }-y&=\frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
175.861 |
|
| \(353\) |
\begin{align*}
y y^{\prime }-y&=A \,x^{2}-\frac {9}{625 A} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
88.698 |
|
| \(354\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
95.212 |
|
| \(355\) |
\begin{align*}
y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
95.165 |
|
| \(356\) |
\begin{align*}
y y^{\prime }-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
138.228 |
|
| \(357\) |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
206.063 |
|
| \(358\) |
\begin{align*}
y y^{\prime }-y&=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
208.263 |
|
| \(359\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
242.517 |
|
| \(360\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+A \sqrt {x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
138.699 |
|
| \(361\) |
\begin{align*}
y y^{\prime }-y&=20 x +\frac {A}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
127.634 |
|
| \(362\) |
\begin{align*}
y y^{\prime }-y&=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
223.219 |
|
| \(363\) |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
245.751 |
|
| \(364\) |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
218.039 |
|
| \(365\) |
\begin{align*}
y y^{\prime }-y&=\frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
150.082 |
|
| \(366\) |
\begin{align*}
y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
210.667 |
|
| \(367\) |
\begin{align*}
y y^{\prime }-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
187.439 |
|
| \(368\) |
\begin{align*}
y y^{\prime }-y&=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
441.402 |
|
| \(369\) |
\begin{align*}
y y^{\prime }-y&=a x +b \,x^{m} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
154.829 |
|
| \(370\) |
\begin{align*}
y y^{\prime }-y&=a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
121.970 |
|
| \(371\) |
\begin{align*}
y y^{\prime }-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
61.809 |
|
| \(372\) |
\begin{align*}
y y^{\prime }&=\left (a x +b \right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
130.379 |
|
| \(373\) |
\begin{align*}
y y^{\prime }&=\frac {y}{\left (a x +b \right )^{2}}+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
96.091 |
|
| \(374\) |
\begin{align*}
y y^{\prime }&=\left (a -\frac {1}{a x}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
154.925 |
|
| \(375\) |
\begin{align*}
y y^{\prime }&=\frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
186.312 |
|
| \(376\) |
\begin{align*}
y y^{\prime }&=\left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
143.617 |
|
| \(377\) |
\begin{align*}
y y^{\prime }&=a \,{\mathrm e}^{\lambda x} y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
63.072 |
|
| \(378\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
94.205 |
|
| \(379\) |
\begin{align*}
y y^{\prime }&=a y \cosh \left (x \right )+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
93.173 |
|
| \(380\) |
\begin{align*}
y y^{\prime }&=a \cos \left (\lambda x \right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
72.616 |
|
| \(381\) |
\begin{align*}
y y^{\prime }&=a \sin \left (\lambda x \right ) y+1 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
165.049 |
|
| \(382\) |
\begin{align*}
y y^{\prime }&=\left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
159.635 |
|
| \(383\) |
\begin{align*}
2 y y^{\prime }&=\left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
142.329 |
|
| \(384\) |
\begin{align*}
y y^{\prime }&=\left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
239.288 |
|
| \(385\) |
\begin{align*}
y y^{\prime }+x \left (a \,x^{2}+b \right ) y+x&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
228.819 |
|
| \(386\) |
\begin{align*}
y y^{\prime }+a \left (1-\frac {1}{x}\right ) y&=a^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
177.737 |
|
| \(387\) |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{x}\right ) y&=a^{2} b \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
185.558 |
|
| \(388\) |
\begin{align*}
y y^{\prime }&=x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (a +x \right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
256.303 |
|
| \(389\) |
\begin{align*}
y y^{\prime }&=a \left (-n b +x \right ) x^{n -1} y+c \left (x^{2}-\left (2 n +1\right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
384.433 |
|
| \(390\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x \left (m -1\right )+1\right ) y}{x}&=\frac {a^{2} \left (x m +1\right ) \left (-1+x \right )}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
127.766 |
|
| \(391\) |
\begin{align*}
y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y&=\frac {a^{2} b}{\sqrt {x}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
219.747 |
|
| \(392\) |
\begin{align*}
y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x}&=-\frac {a^{2} \left (-1+x \right ) \left (4 x -1\right )}{2 x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
183.500 |
|
| \(393\) |
\begin{align*}
y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2}&=\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
153.806 |
|
| \(394\) |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (-1+x \right ) \left (x -6\right )}{15 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
191.611 |
|
| \(395\) |
\begin{align*}
y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}&=a^{2} \left (-x^{2}+1\right ) \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
224.378 |
|
| \(396\) |
\begin{align*}
y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (-1+x \right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
188.330 |
|
| \(397\) |
\begin{align*}
y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}}&=-\frac {a^{2} \left (-1+x \right ) \left (27 x -32\right )}{20 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
191.743 |
|
| \(398\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x +5\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
258.118 |
|
| \(399\) |
\begin{align*}
y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}}&=-\frac {a^{2} \left (-1+x \right ) \left (16 x +5\right )}{14 x^{{9}/{7}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
214.412 |
|
| \(400\) |
\begin{align*}
y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (-1+x \right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
223.599 |
|
| \(401\) |
\begin{align*}
y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x -1\right )}{x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
157.632 |
|
| \(402\) |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (-1+x \right ) \left (8 x -5\right )}{5 x^{7}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
158.275 |
|
| \(403\) |
\begin{align*}
y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (-1+x \right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
217.194 |
|
| \(404\) |
\begin{align*}
y y^{\prime }+\frac {a \left (x -2\right ) y}{x}&=\frac {2 a^{2} \left (-1+x \right )}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
210.671 |
|
| \(405\) |
\begin{align*}
y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x}&=-\frac {2 a^{2} \left (-1+x \right )^{2}}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
188.778 |
|
| \(406\) |
\begin{align*}
y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x}&=\frac {a^{2} b}{x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
151.261 |
|
| \(407\) |
\begin{align*}
y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}}&=\frac {a^{2} \left (-1+x \right ) \left (2+x \right )}{4 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
216.031 |
|
| \(408\) |
\begin{align*}
y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (-1+x \right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
207.556 |
|
| \(409\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}}&=-\frac {a^{2} \left (-1+x \right ) \left (3 x -4\right )}{8 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
237.404 |
|
| \(410\) |
\begin{align*}
y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}}&=-\frac {a^{2} \left (-1+x \right ) \left (x -13\right )}{26 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
230.642 |
|
| \(411\) |
\begin{align*}
y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (-1+x \right ) \left (8 x +1\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
208.808 |
|
| \(412\) |
\begin{align*}
y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (-1+x \right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
221.211 |
|
| \(413\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{{3}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
193.862 |
|
| \(414\) |
\begin{align*}
y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{{11}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
212.066 |
|
| \(415\) |
\begin{align*}
y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}}&=\frac {a^{2} \left (-1+x \right ) \left (1+3 x \right )}{2 x^{4}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
235.979 |
|
| \(416\) |
\begin{align*}
y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (-1+x \right ) \left (x +4\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
214.320 |
|
| \(417\) |
\begin{align*}
y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (-1+x \right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
274.557 |
|
| \(418\) |
\begin{align*}
y y^{\prime }-\frac {a \left (\left (1+k \right ) x -1\right ) y}{x^{2}}&=\frac {a^{2} \left (1+k \right ) \left (-1+x \right )}{x^{2}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
347.522 |
|
| \(419\) |
\begin{align*}
y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y&=n \left (x -a \right ) x^{-2 n} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
409.132 |
|
| \(420\) |
\begin{align*}
y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y&=-\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
360.287 |
|
| \(421\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
169.225 |
|
| \(422\) |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
271.728 |
|
| \(423\) |
\begin{align*}
y y^{\prime }&={\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
375.302 |
|
| \(424\) |
\begin{align*}
y y^{\prime }&={\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
258.804 |
|
| \(425\) |
\begin{align*}
y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y&=-a^{2} b \,x^{2} {\mathrm e}^{2 b x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
168.952 |
|
| \(426\) |
\begin{align*}
y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y&=-a^{2} n \left (n +1\right ) \left (x n +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
212.772 |
|
| \(427\) |
\begin{align*}
y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y&=-a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
233.268 |
|
| \(428\) |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✗ |
✗ |
214.227 |
|
| \(429\) |
\begin{align*}
y y^{\prime }&=\left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right ) \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
218.308 |
|
| \(430\) |
\begin{align*}
y y^{\prime }&=a x \cos \left (\lambda \,x^{2}\right ) y+x \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
268.474 |
|
| \(431\) |
\begin{align*}
y y^{\prime } x&=a y^{2}+b y+c \,x^{n}+s \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
272.214 |
|
| \(432\) |
\begin{align*}
y y^{\prime } x&=-n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
190.739 |
|
| \(433\) |
\begin{align*}
2 y y^{\prime } x&=\left (1-n \right ) y^{2}+\left (a \left (2 n +1\right ) x +2 n -1\right ) y-a^{2} n \,x^{2}-b x -n \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
193.888 |
|
| \(434\) |
\begin{align*}
\left (a x y-a k y+b x -b k \right ) y^{\prime }&=c y^{2}+d x y+\left (-d k +b \right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
170.129 |
|
| \(435\) |
\begin{align*}
\left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+c x y+d \,x^{2}+\left (-A \beta +k \right ) y-c \beta x -k \beta \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
242.013 |
|
| \(436\) |
\begin{align*}
\left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
218.240 |
|
| \(437\) |
\begin{align*}
\left (\left (a x +c \right ) y+\left (1-n \right ) x^{2}+\left (2 n -1\right ) x -n \right ) y^{\prime }&=2 a y^{2}+2 y x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
363.816 |
|
| \(438\) |
\begin{align*}
x \left (\left (m -1\right ) \left (A x +B \right ) y+m \left (d \,x^{2}+e x +F \right )\right ) y^{\prime }&=\left (A \left (1-n \right ) x -B n \right ) y^{2}+\left (d \left (2-n \right ) x^{2}+e \left (1-n \right ) x -F n \right ) y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
968.244 |
|
| \(439\) |
\begin{align*}
x \left (2 a x y+b \right ) y^{\prime }&=-4 a \,x^{2} y^{2}-3 b x y+c \,x^{2}+k \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
142.018 |
|
| \(440\) |
\begin{align*}
\left (y x +a \,x^{n}+b \,x^{2}\right ) y^{\prime }&=y^{2}+c \,x^{n}+b x y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
498.445 |
|
| \(441\) |
\begin{align*}
y y^{\prime }&=-n y^{2}+a \left (2 n +1\right ) {\mathrm e}^{x} y+b y-a^{2} n \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}+c \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
238.633 |
|
| \(442\) |
\begin{align*}
y^{\prime }&=-y^{3}+3 y a^{2} x^{2}-2 a^{3} x^{3}+a \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
47.571 |
|
| \(443\) |
\begin{align*}
y^{\prime }&=-y^{3}+\left (a x +b \right ) y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
100.781 |
|
| \(444\) |
\begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\left (a x +b \right )^{2}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
64.329 |
|
| \(445\) |
\begin{align*}
y^{\prime }&=a y^{3} x +2 a b \,x^{2} y^{2}-b -2 a \,b^{3} x^{4} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
60.346 |
|
| \(446\) |
\begin{align*}
9 y^{\prime }&=-x^{m} \left (a \,x^{-m +1}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{-m +1}+b \right )^{-\lambda -2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
179.393 |
|
| \(447\) |
\begin{align*}
x^{2} y^{\prime }&=y^{3}-3 a^{2} x^{4} y+2 a^{3} x^{6}+2 a \,x^{3} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✗ |
21.972 |
|
| \(448\) |
\begin{align*}
y^{\prime }&=-\left (a x +b \,x^{m}\right ) y^{3}+y^{2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
182.515 |
|
| \(449\) |
\begin{align*}
y^{\prime }&=\frac {y^{3}}{\sqrt {a \,x^{2}+b x +c}}+y^{2} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
163.788 |
|
| \(450\) |
\begin{align*}
y^{\prime }&=-y^{3}+a \,{\mathrm e}^{\lambda x} y^{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
54.804 |
|
| \(451\) |
\begin{align*}
y^{\prime }&=-y^{3}+3 a^{2} {\mathrm e}^{2 \lambda x} y-2 a^{3} {\mathrm e}^{3 \lambda x}+a \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✗ |
26.172 |
|
| \(452\) |
\begin{align*}
\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )&=\left (x^{2}+y^{2}+x \right ) \left (-y+y^{\prime } x \right ) \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
34.281 |
|
| \(453\) |
\begin{align*}
x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
28.636 |
|
| \(454\) |
\begin{align*}
\left (x -y^{\prime }-y\right )^{2}&=x^{2} \left (2 y x -x^{2} y^{\prime }\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
286.203 |
|
| \(455\) |
\begin{align*}
x x^{\prime }&=1-t x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
215.102 |
|
| \(456\) |
\begin{align*}
{x^{\prime }}^{2}+t x&=\sqrt {1+t} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
258.017 |
|
| \(457\) |
\begin{align*}
3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
100.546 |
|
| \(458\) |
\begin{align*}
y^{\prime }&=x y^{3}+x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
92.749 |
|
| \(459\) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
6.202 |
|
| \(460\) |
\begin{align*}
y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
145.259 |
|
| \(461\) |
\begin{align*}
y^{\prime }&=\ln \left (y x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
18.904 |
|
| \(462\) |
\begin{align*}
{y^{\prime }}^{2}+x y {y^{\prime }}^{2}&=\ln \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
413.188 |
|
| \(463\) |
\begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
49.424 |
|
| \(464\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {15-x^{2}-y^{2}}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
64.154 |
|
| \(465\) |
\begin{align*}
y^{\prime }&=2 y^{3}+t^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
25.818 |
|
| \(466\) |
\begin{align*}
y^{\prime }&=\left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
38.137 |
|
| \(467\) |
\begin{align*}
y^{\prime }&=\left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
71.422 |
|
| \(468\) |
\begin{align*}
\sin \left (x +y\right )-y y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
246.785 |
|
| \(469\) |
\begin{align*}
y^{2} y^{\prime }+3 x^{2} y&=\sin \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
136.642 |
|
| \(470\) |
\begin{align*}
4 \left (x^{2}+y^{2}\right ) x -5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
171.687 |
|
| \(471\) |
\begin{align*}
y^{\prime }+t^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
129.788 |
|
| \(472\) |
\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 |
|
| \(473\) |
\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 |
|
| \(474\) |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
12.241 |
|
| \(475\) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
5.167 |
|
| \(476\) |
\begin{align*}
y^{\prime }-2 \,{\mathrm e}^{x} y&=2 \sqrt {{\mathrm e}^{x} y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
92.092 |
|
| \(477\) |
\begin{align*}
y^{\prime }&=y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
47.537 |
|
| \(478\) |
\begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
77.393 |
|
| \(479\) |
\begin{align*}
y^{\prime }&=\sqrt {1-t^{2}-y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
59.336 |
|
| \(480\) |
\begin{align*}
y^{\prime }&=\frac {\ln \left (t y\right )}{1-t^{2}+y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
132.326 |
|
| \(481\) |
\begin{align*}
y^{\prime }&=\left (t^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
60.402 |
|
| \(482\) |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
23.737 |
|
| \(483\) |
\begin{align*}
\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
41.940 |
|
| \(484\) |
\begin{align*}
\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
50.277 |
|
| \(485\) |
\begin{align*}
y&={y^{\prime }}^{2}-y^{\prime } x +\frac {x^{3}}{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
382.467 |
|
| \(486\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
684.507 |
|
| \(487\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
509.422 |
|
| \(488\) |
\begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
716.943 |
|
| \(489\) |
\begin{align*}
y^{\prime }-\frac {\tan \left (y\right )}{x +1}&=\left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
71.453 |
|
| \(490\) |
\begin{align*}
y^{\prime }+\frac {y \ln \left (y\right )}{x}&=\frac {y}{x^{2}}-\ln \left (y\right )^{2} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
82.006 |
|
| \(491\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \left ({\mathrm e}^{x}-{\mathrm e}^{y}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
31.893 |
|
| \(492\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
682.009 |
|
| \(493\) |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&={y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
521.882 |
|
| \(494\) |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}-h^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
498.173 |
|
| \(495\) |
\begin{align*}
\left (x^{2} y^{\prime }+y^{2}\right ) \left (y^{\prime } x +y\right )&=\left (1+y^{\prime }\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
451.090 |
|
| \(496\) |
\begin{align*}
\left (x y \sin \left (y x \right )+\cos \left (y x \right )\right ) y+\left (x y \sin \left (y x \right )-\cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
34.044 |
|
| \(497\) |
\begin{align*}
3 x^{2} y^{4}+2 y x +\left (2 x^{3} y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
101.466 |
|
| \(498\) |
\begin{align*}
3 y {y^{\prime }}^{2}-2 y y^{\prime } x +4 y^{2}-x^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
916.148 |
|
| \(499\) |
\begin{align*}
\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✗ |
731.178 |
|
| \(500\) |
\begin{align*}
\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
465.243 |
|
| \(501\) |
\begin{align*}
3 x^{2}+6 x y^{2}+\left (6 x^{2}+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
81.386 |
|
| \(502\) |
\begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
36.861 |
|
| \(503\) |
\begin{align*}
y^{\prime }&=x +\sqrt {1+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
119.125 |
|
| \(504\) |
\begin{align*}
x^{\prime }&=t^{2} x^{4}+1 \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
31.166 |
|
| \(505\) |
\begin{align*}
x^{\prime }&=\sin \left (t x\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
7.032 |
|
| \(506\) |
\begin{align*}
x^{\prime }&=\arctan \left (x\right )+t \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
86.876 |
|
| \(507\) |
\begin{align*}
x^{2}+y^{2}+\left (a x y+y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
126.747 |
|
| \(508\) |
\begin{align*}
{x^{\prime }}^{2}&=x^{2}+t^{2}-1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
119.299 |
|
| \(509\) |
\begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✗ |
73.177 |
|
| \(510\) |
\begin{align*}
y^{\prime }&=1+x +x^{2} \cos \left (x \right )-\left (1+4 \cos \left (x \right ) x \right ) y+2 y^{2} \cos \left (x \right ) \\
\end{align*} |
[_Riccati] |
✗ |
✗ |
✗ |
276.846 |
|
| \(511\) |
\begin{align*}
\frac {x^{2}}{y}+y^{2}-\left (\frac {x^{3}}{y^{2}}+y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✗ |
53.993 |
|
| \(512\) |
\begin{align*}
a x y-b +\left (c x y-d \right ) x y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
199.642 |
|
| \(513\) |
\begin{align*}
y^{\prime }&=x \sin \left (y\right )+{\mathrm e}^{x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
24.087 |
|
| \(514\) |
\begin{align*}
1+y x +y y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
297.357 |
|
| \(515\) |
\begin{align*}
{| y^{\prime }|}+1&=0 \\
\end{align*} |
[_sym_implicit] |
✓ |
✗ |
✗ |
1.833 |
|
| \(516\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
172.194 |
|
| \(517\) |
\begin{align*}
y^{\prime }&=y \csc \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✗ |
✗ |
✗ |
86.890 |
|
| \(518\) |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {x^{2}+4 y^{2}-4}} \\
y \left (3\right ) &= 2 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
69.819 |
|
| \(519\) |
\begin{align*}
U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✗ |
122.749 |
|
| \(520\) |
\begin{align*}
x^{2}+y \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )-\left (x^{2}+x \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
183.758 |
|
| \(521\) |
\begin{align*}
y^{\prime }&=\sqrt {y+\sin \left (x \right )}-\cos \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
165.441 |
|
| \(522\) |
\begin{align*}
y^{\prime } x +y&=3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✗ |
✗ |
✓ |
188.144 |
|
| \(523\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
175.376 |
|
| \(524\) |
\begin{align*}
y y^{\prime }&=y+x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
184.287 |
|
| \(525\) |
\begin{align*}
y^{2} y^{\prime }+\tan \left (x \right ) y&=\sin \left (x \right )^{3} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
222.683 |
|
| \(526\) |
\begin{align*}
{\mathrm e}^{x} \cos \left (y\right )-x^{2}+\left ({\mathrm e}^{y} \sin \left (x \right )+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
149.507 |
|
| \(527\) |
\begin{align*}
2 x -3 y+\left (7 y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
98.502 |
|
| \(528\) |
\begin{align*}
y x +1+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
237.146 |
|
| \(529\) |
\begin{align*}
2 x^{3} y+\left (2 y^{2} x^{2}+2 y^{4}+\ln \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
263.238 |
|
| \(530\) |
\begin{align*}
y^{\prime }&=\frac {y x +3}{5 x -y} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
216.405 |
|
| \(531\) |
\begin{align*}
y^{\prime }&=\frac {2 y x +3 y}{x^{2}+2 y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
113.521 |
|
| \(532\) |
\begin{align*}
\frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
80.013 |
|
| \(533\) |
\begin{align*}
x^{2} y+\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
129.964 |
|
| \(534\) |
\begin{align*}
x^{3}+y^{2}+\left (y x -3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
154.648 |
|
| \(535\) |
\begin{align*}
x +\sin \left (y\right )-\cos \left (y\right )-x \cos \left (y\right ) \left (2 x \sin \left (y\right )+1\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
200.129 |
|
| \(536\) |
\begin{align*}
y^{2} \left (-x^{2}+1\right )+x \left (y^{2} x^{2}+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
61.026 |
|
| \(537\) |
\begin{align*}
y \left (y^{2} x^{2}-1\right )+x \left (x^{2} y+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
189.018 |
|
| \(538\) |
\begin{align*}
y \left (x \tan \left (x \right )+\ln \left (y\right )\right )+\tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
97.137 |
|
| \(539\) |
\begin{align*}
y^{\prime }&=\tan \left (y\right ) \cot \left (x \right )-\sec \left (y\right ) \cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
68.766 |
|
| \(540\) |
\begin{align*}
{y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
928.867 |
|
| \(541\) |
\begin{align*}
y+2 t +2 t y y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
374.353 |
|
| \(542\) |
\begin{align*}
2 t^{2}-y+\left (t +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
49.593 |
|
| \(543\) |
\begin{align*}
y^{\prime }&=6 \sqrt {y}+5 x^{3} \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
79.575 |
|
| \(544\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✗ |
109.538 |
|
| \(545\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
21.160 |
|
| \(546\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
20.199 |
|
| \(547\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
19.495 |
|
| \(548\) |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (8\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
21.071 |
|
| \(549\) |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✗ |
186.438 |
|
| \(550\) |
\begin{align*}
y^{\prime }-2 y x&=6 y \,{\mathrm e}^{y^{2}} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
108.674 |
|
| \(551\) |
\begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
10.822 |
|
| \(552\) |
\begin{align*}
{\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✗ |
✗ |
✗ |
97.371 |
|
| \(553\) |
\begin{align*}
\left (x +1\right ) y^{\prime }&=-1+y \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
122.797 |
|
| \(554\) |
\begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
108.571 |
|
| \(555\) |
\begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
109.691 |
|
| \(556\) |
\begin{align*}
y^{\prime }-2 y x&=\cos \left (x \right )-2 x \sin \left (x \right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_linear] |
✓ |
✗ |
✓ |
97.681 |
|
| \(557\) |
\begin{align*}
2 \sqrt {x}\, y^{\prime }-y&=-\sin \left (\sqrt {x}\right )-\cos \left (\sqrt {x}\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_linear] |
✓ |
✗ |
✓ |
241.758 |
|
| \(558\) |
\begin{align*}
y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✗ |
✓ |
100.338 |
|
| \(559\) |
\begin{align*}
\left (x^{2}+1\right ) \ln \left (x^{2}+1\right ) y^{\prime }-2 y x&=\ln \left (x^{2}+1\right )-2 x \arctan \left (x \right ) \\
y \left (-\infty \right ) &= -\frac {\pi }{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
265.334 |
|
| \(560\) |
\begin{align*}
y^{\prime } \cos \left (y\right )&=\sin \left (x +y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
40.283 |
|
| \(561\) |
\begin{align*}
y^{\prime }&=\frac {\left (x +1\right )^{2}-2 y}{2 y} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
275.089 |
|
| \(562\) |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{x}-\sin \left (y\right ) \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
28.624 |
|
| \(563\) |
\begin{align*}
\left (\cos \left (x +y\right )+\sin \left (x -y\right )\right ) y^{\prime }&=\cos \left (2 x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
159.933 |
|
| \(564\) |
\begin{align*}
\ln \left (y^{x}\right ) y^{\prime }&=3 x^{2} y \\
y \left (2\right ) &= {\mathrm e}^{3} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
420.029 |
|
| \(565\) |
\begin{align*}
4 y x +2 x^{2}+y+\left (2 x^{2}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
48.353 |
|
| \(566\) |
\begin{align*}
y^{\prime }+\frac {1}{x}&=\frac {2}{x^{3} y^{{4}/{3}}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
65.824 |
|
| \(567\) |
\begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
9.461 |
|
| \(568\) |
\begin{align*}
y^{\prime }&=x^{2}-y^{2}+\frac {8 x}{y} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
214.281 |
|
| \(569\) |
\begin{align*}
y^{\prime }&=\cos \left ({\mathrm e}^{y x}\right ) \\
y \left (0\right ) &= -4 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
37.899 |
|
| \(570\) |
\begin{align*}
\left (x^{3}+3 \ln \left (y\right )\right ) y&=y^{\prime } x \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
89.864 |
|
| \(571\) |
\begin{align*}
y \left (x +y^{2}\right )+x^{2} \left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✗ |
280.107 |
|
| \(572\) |
\begin{align*}
x^{2}-y+x \left (1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✗ |
✗ |
143.173 |
|
| \(573\) |
\begin{align*}
y^{\prime }&=y^{2}-3 x^{2}-1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
|
✗ |
✓ |
✗ |
178.353 |
|
| \(574\) |
\begin{align*}
x^{3}-2 x y^{2}+3 x^{2} y y^{\prime }&=-y+y^{\prime } x \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
186.388 |
|
| \(575\) |
\begin{align*}
y^{\prime } x&=\left (x^{2}+\tan \left (y\right )\right ) \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
50.030 |
|
| \(576\) |
\begin{align*}
y^{\prime }&=\frac {\left (3 x +y^{3}-1\right )^{2}}{y^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
244.022 |
|
| \(577\) |
\begin{align*}
y y^{\prime } x -x^{2} \sqrt {1+y^{2}}&=\left (x +1\right ) \left (1+y^{2}\right ) \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
223.886 |
|
| \(578\) |
\begin{align*}
\left (3 y x +x +y\right ) y+\left (4 y x +x +2 y\right ) x y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✗ |
292.425 |
|
| \(579\) |
\begin{align*}
x^{2}-1+\left (y^{2} x^{2}+x^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
66.754 |
|