ﬁrst order ode homogD2

Table 2.407: ﬁrst order ode homogD2


#	ODE	CAS classiﬁcation	Solved?

23	$y^{'} = y - x + 1$	[[_linear, ‘class A‘]]	✓

24	$y^{'} = x - y + 1$	[[_linear, ‘class A‘]]	✓

41	$y^{'} + 2 x y = 0$	[_separable]	✓

43	$y^{'} = y \sin (x)$	[_separable]	✓

44	$(x + 1) y^{'} = 4 y$	[_separable]	✓

49	$(- x^{2} + 1) y^{'} = 2 y$	[_separable]	✓

59	$y^{'} = y e^{x}$ i.c.	[_separable]	✓

62	$y^{'} = 4 x^{3} y - y$ i.c.	[_separable]	✓

64	$\tan (x) y^{'} = y$ i.c.	[_separable]	✓

65	$- y + x y^{'} = 2 x^{2} y$ i.c.	[_separable]	✓

77	$x y^{'} + 2 y = 3 x$ i.c.	[_linear]	✓

80	$3 x y^{'} + y = 12 x$	[_linear]	✓

81	$- y + x y^{'} = x$ i.c.	[_linear]	✓

103	$y^{'} + p (x) y = 0$	[_separable]	✓

105	$(x + y) y^{'} = x - y$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

106	$2 x y y^{'} = x^{2} + 2 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

108	$y^{'} (x - y) = x + y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

109	$x (x + y) y^{'} = y (x - y)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

110	$(x + 2 y) y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

111	$x y^{2} y^{'} = x^{3} + y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

112	$x^{2} y^{'} = x y + x^{2} e^{\frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

113	$x^{2} y^{'} = x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

114	$x y y^{'} = x^{2} + 3 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

115	$(x^{2} - y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

119	$x (x + y) y^{'} + y (3 x + y) = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

135	$2 x + 3 y + (3 x + 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

136	$4 x - y + (6 y - x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

137	$3 x^{2} + 2 y^{2} + (4 x y + 6 y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

146	$\frac{2 x^{5 / 2} - 3 y^{5 / 3}}{2 x^{5 / 2} y^{2 / 3}} + \frac{(3 y^{5 / 3} - 2 x^{5 / 2}) y^{'}}{3 x^{3 / 2} y^{5 / 3}} = 0$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓

166	$y^{'} = - \frac{y (2 x^{3} - y^{3})}{x (2 y^{3} - x^{3})}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

181	$x y + y^{2} - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

183	$3 y + x^{4} y^{'} = 2 x y$	[_separable]	✓

186	$2 x y + x^{2} y^{'} = y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

189	$x^{2} y^{'} = x y + 3 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

190	$6 x y^{3} + 2 y^{4} + (9 y^{2} x^{2} + 8 x y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

192	$x^{3} y^{'} = x^{2} y - y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

196	$2 x^{2} y - x^{3} y^{'} = y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

211	$y^{'} = - \frac{3 x^{2} + 2 y^{2}}{4 x y}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

212	$y^{'} = \frac{x + 3 y}{y - 3 x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

665	$y^{'} = y - x + 1$	[[_linear, ‘class A‘]]	✓

666	$y^{'} = x - y + 1$	[[_linear, ‘class A‘]]	✓

677	$y^{'} + 2 x y = 0$	[_separable]	✓

679	$y^{'} = y \sin (x)$	[_separable]	✓

680	$(x + 1) y^{'} = 4 y$	[_separable]	✓

685	$(- x^{2} + 1) y^{'} = 2 y$	[_separable]	✓

694	$y^{'} = y e^{x}$ i.c.	[_separable]	✓

697	$y^{'} = 4 x^{3} y - y$ i.c.	[_separable]	✓

699	$\tan (x) y^{'} = y$ i.c.	[_separable]	✓

700	$- y + x y^{'} = 2 x^{2} y$ i.c.	[_separable]	✓

708	$x y^{'} + 2 y = 3 x$ i.c.	[_linear]	✓

711	$3 x y^{'} + y = 12 x$	[_linear]	✓

712	$- y + x y^{'} = x$ i.c.	[_linear]	✓

729	$(x + y) y^{'} = x - y$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

730	$2 x y y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

732	$y^{'} (x - y) = x + y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

733	$x (x + y) y^{'} = y (x - y)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

734	$(x + 2 y) y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

735	$x y^{2} y^{'} = x^{3} + y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

736	$x^{2} y^{'} = x y + x^{2} e^{\frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

737	$x^{2} y^{'} = x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

738	$x y y^{'} = x^{2} + 3 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

739	$(x^{2} - y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

743	$x (x + y) y^{'} + y (3 x + y) = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

746	$(x + y) y^{'} = 0$	[_quadrature]	✓

759	$2 x + 3 y + (3 x + 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

760	$4 x - y + (6 y - x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

761	$3 x^{2} + 2 y^{2} + (4 x y + 6 y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

770	$\frac{2 x^{5 / 2} - 3 y^{5 / 3}}{2 x^{5 / 2} y^{2 / 3}} + \frac{(3 y^{5 / 3} - 2 x^{5 / 2}) y^{'}}{3 x^{3 / 2} y^{5 / 3}} = 0$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓

773	$x y + y^{2} - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

775	$3 y + x^{4} y^{'} = 2 x y$	[_separable]	✓

778	$2 x y + x^{2} y^{'} = y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

781	$x^{2} y^{'} = x y + 3 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

782	$6 x y^{3} + 2 y^{4} + (9 y^{2} x^{2} + 8 x y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

784	$x^{3} y^{'} = x^{2} y - y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

788	$2 x^{2} y - x^{3} y^{'} = y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

803	$y^{'} = \frac{- 3 x^{2} - 2 y^{2}}{4 x y}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

804	$y^{'} = \frac{x + 3 y}{y - 3 x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1107	$- y + t y^{'} = t^{2} e^{- t}$	[_linear]	✓

1158	$y^{'} = \frac{y^{2} + x y + x^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

1159	$y^{'} = \frac{x^{2} + 3 y^{2}}{2 x y}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1160	$y^{'} = \frac{4 y - 3 x}{2 x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1161	$y^{'} = - \frac{4 x + 3 y}{2 x + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1162	$y^{'} = \frac{x + 3 y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1163	$x^{2} + 3 x y + y^{2} - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

1164	$y^{'} = \frac{x^{2} - 3 y^{2}}{2 x y}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1165	$y^{'} = \frac{3 y^{2} - x^{2}}{2 x y}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1167	$t (- 4 + t) y^{'} + y = 0$ i.c.	[_separable]	✓

1174	$y^{'} = - \frac{4 t}{y}$	[_separable]	✓

1194	$2 x + 4 y + (2 x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1196	$2 y + 2 x y^{2} + (2 x^{2} y + 2 x) y^{'} = 0$	[_separable]	✓

1197	$y^{'} = \frac{- a x - b y}{b x + c y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1198	$y^{'} = \frac{- a x + b y}{b x - c y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1204	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓

1205	$2 x - y + (- x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1210	$2 x y + 3 x^{2} y + y^{3} + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational]	✓

1217	$3 x y + y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

1231	$x + y + (x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1232	$(e^{x} + 1) y^{'} = y - y e^{x}$	[_separable]	✓

1243	$x y^{'} = e^{\frac{y}{x}} x + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

1245	$3 t + 2 y = - t y^{'}$	[_linear]	✓

1246	$y^{'} = \frac{x + y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1247	$2 x y + 3 y^{2} - (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

1519	$y^{'} = 2 y$	[_quadrature]	✓

1537	$y^{'} + a y = 0$	[_quadrature]	✓

1538	$y^{'} + 3 x^{2} y = 0$	[_separable]	✓

1539	$x y^{'} + y \ln (x) = 0$	[_separable]	✓

1540	$x y^{'} + 3 y = 0$	[_separable]	✓

1541	$x^{2} y^{'} + y = 0$	[_separable]	✓

1542	$y^{'} + \frac{(x + 1) y}{x} = 0$ i.c.	[_separable]	✓

1543	$x y^{'} + (1 + \frac{1}{\ln (x)}) y = 0$ i.c.	[_separable]	✓

1544	$x y^{'} + (1 + x \cot (x)) y = 0$ i.c.	[_separable]	✓

1545	$y^{'} - \frac{2 x y}{x^{2} + 1} = 0$ i.c.	[_separable]	✓

1546	$y^{'} + \frac{k y}{x} = 0$ i.c.	[_separable]	✓

1547	$y^{'} + \tan (k x) y = 0$ i.c.	[_separable]	✓

1584	$y^{'} (x^{2} + 1) + x y = 0$	[_separable]	✓

1597	$x + y y^{'} = 0$ i.c.	[_separable]	✓

1599	$(x + 1) (- 2 + x) y^{'} + y = 0$ i.c.	[_separable]	✓

1613	$y^{'} = 2 x y$	[_separable]	✓

1615	$y^{'} = \frac{2 x + 3 y}{x - 4 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1626	$y^{'} = \frac{y + x e^{- \frac{y}{x}}}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

1628	$x^{2} y^{'} = y^{2} + x y - x^{2}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

1642	$y^{'} = \frac{x + y}{x}$	[_linear]	✓

1643	$y^{'} = \frac{2 x y + y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1644	$x y^{3} y^{'} = y^{4} + x^{4}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1645	$y^{'} = \frac{y}{x} + \sec (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

1646	$x^{2} y^{'} = y^{2} + x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

1647	$x y y^{'} = x^{2} + 2 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1648	$y^{'} = \frac{2 y^{2} + x^{2} e^{- \frac{y^{2}}{x^{2}}}}{2 x y}$	[[_homogeneous, ‘class A‘]]	✓

1649	$y^{'} = \frac{x y + y^{2}}{x^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1650	$y^{'} = \frac{x^{3} + y^{3}}{x y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1651	$x y y^{'} + x^{2} + y^{2} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1652	$y^{'} = \frac{y^{2} - 3 x y - 5 x^{2}}{x^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

1653	$x^{2} y^{'} = 2 x^{2} + y^{2} + 4 x y$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

1654	$x y y^{'} = 3 x^{2} + 4 y^{2}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

1655	$y^{'} = \frac{x + y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1657	$y^{'} = \frac{y^{3} + 2 x y^{2} + x^{2} y + x^{3}}{x {(x + y)}^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

1658	$y^{'} = \frac{x + 2 y}{2 x + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1659	$y^{'} = \frac{y}{- 2 x + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1660	$y^{'} = \frac{x y^{2} + 2 y^{3}}{x^{3} + x^{2} y + x y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

1661	$y^{'} = \frac{x^{3} + x^{2} y + 3 y^{3}}{x^{3} + 3 x y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

1662	$x^{2} y^{'} = y^{2} + x y - 4 x^{2}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

1663	$x y y^{'} = x^{2} - x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

1664	$y^{'} = \frac{2 y^{2} - x y + 2 x^{2}}{x y + 2 x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

1665	$y^{'} = \frac{y^{2} + x y + x^{2}}{x y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

1680	$6 y^{2} x^{2} + 4 x^{3} y y^{'} = 0$	[_separable]	✓

1682	$14 x^{2} y^{3} + 21 x^{2} y^{2} y^{'} = 0$	[_quadrature]	✓

1684	${(x + y)}^{2} + {(x + y)}^{2} y^{'} = 0$	[_quadrature]	✓

1685	$4 x + 7 y + (4 y + 3 x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1687	$2 x + y + (2 y + 2 x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1692	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓

1702	$7 x + 4 y + (4 x + 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

1707	$x^{2} + y^{2} + 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓

1712	$x^{2} y^{'} - y^{2} = 0$	[_separable]	✓

1713	$y - x y^{'} = 0$	[_separable]	✓

1714	$3 x^{2} y + 2 x^{3} y^{'} = 0$	[_separable]	✓

1715	$2 y^{3} + 3 y^{2} y^{'} = 0$	[_quadrature]	✓

1718	$27 x y^{2} + 8 y^{3} + (18 x^{2} y + 12 x y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

1722	$x^{2} y + 4 x y + 2 y + (x^{2} + x) y^{'} = 0$	[_separable]	✓

1723	$- y + (x^{4} - x) y^{'} = 0$	[_separable]	✓

1731	$x^{4} y^{4} + x^{5} y^{3} y^{'} = 0$	[_separable]	✓

1734	$3 x y + 2 y^{2} + y + (x^{2} + 2 x y + x + 2 y) y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

2299	$\cos (t) y + y^{'} = 0$	[_separable]	✓

2300	$\sqrt{t} \sin (t) y + y^{'} = 0$	[_separable]	✓

2306	$\sqrt{t^{2} + 1} y + y^{'} = 0$ i.c.	[_separable]	✓

2307	$\sqrt{t^{2} + 1} y e^{- t} + y^{'} = 0$	[_separable]	✓

2331	$2 t y y^{'} = 3 y^{2} - t^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

2333	$y^{'} = \frac{y + t}{- y + t}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2334	$e^{\frac{t}{y}} (- t + y) y^{'} + y (1 + e^{\frac{t}{y}}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2342	$2 t y^{3} + 3 t^{2} y^{2} y^{'} = 0$ i.c.	[_separable]	✓

2346	$3 t y + y^{2} + (t^{2} + t y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

2472	$\cos (t) y + y^{'} = 0$	[_separable]	✓

2473	$\sqrt{t} \sin (t) y + y^{'} = 0$	[_separable]	✓

2479	$\sqrt{t^{2} + 1} y + y^{'} = 0$ i.c.	[_separable]	✓

2480	$\sqrt{t^{2} + 1} y e^{- t} + y^{'} = 0$ i.c.	[_separable]	✓

2481	$\sqrt{t^{2} + 1} y e^{- t} + y^{'} = 0$ i.c.	[_separable]	✓

2501	$y^{'} = \frac{2 y}{t} + \frac{y^{2}}{t^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

2503	$2 t y y^{'} = 3 y^{2} - t^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

2505	$y^{'} = \frac{y + t}{- y + t}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2506	$e^{\frac{t}{y}} (- t + y) y^{'} + y (1 + e^{\frac{t}{y}}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2514	$2 t y^{3} + 3 t^{2} y^{2} y^{'} = 0$ i.c.	[_separable]	✓

2518	$3 t y + y^{2} + (t^{2} + t y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

2841	$y^{'} (x^{2} + 1) + x y = 0$	[_separable]	✓

2842	$x y^{2} + x + (y - x^{2} y) y^{'} = 0$	[_separable]	✓

2844	$x y^{'} + y = 0$	[_separable]	✓

2845	$y^{'} = 2 x y$	[_separable]	✓

2851	$y^{'} = \frac{x}{y}$	[_separable]	✓

2857	$x y + \sqrt{x^{2} + 1} y^{'} = 0$	[_separable]	✓

2858	$y = x y + x^{2} y^{'}$	[_separable]	✓

2861	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

2862	$x y^{'} + 2 y = 0$ i.c.	[_separable]	✓

2864	$x^{2} y^{'} + y^{2} = 0$ i.c.	[_separable]	✓

2871	$x + y = x y^{'}$	[_linear]	✓

2872	$(x + y) y^{'} + x = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2874	$y^{'} = \frac{2 x - y}{x + 4 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2876	$x + y y^{'} = 2 y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2878	$x^{2} + y^{2} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

2879	$(x y - x^{2}) y^{'} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

2881	$x + y + y^{'} (x - y) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2882	$y (x^{2} - x y + y^{2}) + x y^{'} (y^{2} + x y + x^{2}) = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓


2883	$x y^{'} - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2884	$y^{'} = \frac{y}{x} + \cosh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2885	$x^{2} + y^{2} = 2 x y y^{'}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

2886	$(\frac{x}{y} + \frac{y}{x}) y^{'} + 1 = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

2887	$e^{\frac{y}{x}} x + y = x y^{'}$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2888	$y^{'} = \frac{x + y}{x - y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2889	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2890	$(3 x y - 2 x^{2}) y^{'} = 2 y^{2} - x y$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

2892	$y^{2} (y y^{'} - x) + x^{3} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

2893	$y^{'} = \frac{y}{x} + \tanh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

2914	$x + y + (x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2915	$3 x + y + (x + 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2919	$2 x y - (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

2921	$\frac{2 x y - 1}{y} + \frac{(x + 3 y) y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2925	$\frac{2}{y} - \frac{y}{x^{2}} + (\frac{1}{x} - \frac{2 x}{y^{2}}) y^{'} = 0$	[_separable]	✓

2926	$\frac{1 + x y}{y} + \frac{(- x + 2 y) y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2934	$\frac{x^{2} + 3 y^{2}}{x (3 x^{2} + 4 y^{2})} + \frac{(2 x^{2} + y^{2}) y^{'}}{y (3 x^{2} + 4 y^{2})} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

2935	$\frac{x^{2} - y^{2}}{x (2 x^{2} + y^{2})} + \frac{(x^{2} + 2 y^{2}) y^{'}}{y (2 x^{2} + y^{2})} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

2937	$x y^{'} + \ln (x) - y = 0$	[_linear]	✓

2943	$y (y - x^{2}) + x^{3} y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

2951	$2 x^{2} y y^{'} + x^{4} e^{x} - 2 x y^{2} = 0$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓

2953	$y (x^{2} - 1) + x (x^{2} + 1) y^{'} = 0$ i.c.	[_separable]	✓

2964	$y + (2 x - 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

2986	$x y y^{'} = x^{2} - y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

2989	$x^{2} y^{'} + y^{2} = x y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

3005	$y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

3006	$2 x + y - (x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3014	$x^{2} y - (x^{3} + y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

3019	$y + (- 2 y + 3 x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3020	$r^{'} = r \cot (θ)$	[_separable]	✓

3021	$(4 y + 3 x) y^{'} + 2 x + y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3026	$1 + e^{\frac{x}{y}} + e^{\frac{x}{y}} (1 - \frac{x}{y}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓

3036	$y \cos (\frac{x}{y}) - (y + x \cos (\frac{x}{y})) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

3041	$x y - y^{2} - x^{2} y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

3045	$(- 2 x^{2} - 3 x y) y^{'} + y^{2} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

3049	$x^{2} + y^{2} = 2 x y y^{'}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

3050	$3 x y + (3 x^{2} + y^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

3056	$y^{3} + 2 x^{2} y + (- 3 x^{3} - 2 x y^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

3058	$y^{'} - y = 0$	[_quadrature]	✓

3403	$y^{'} = 2$	[_quadrature]	✓

3409	$y^{'} = x y$	[_separable]	✓

3431	$y^{'} = \frac{y}{t}$	[_separable]	✓

3432	$y^{'} = - \frac{t}{y}$	[_separable]	✓

3438	$y^{'} = (t^{2} + 1) y$	[_separable]	✓

3439	$y^{'} = - y$	[_quadrature]	✓

3447	$y^{'} = y$ i.c.	[_quadrature]	✓

3448	$y^{'} = 2 y$ i.c.	[_quadrature]	✓

3449	$t y^{'} = y + t^{3}$ i.c.	[_linear]	✓

3451	$y^{'} = \frac{2 y}{t + 1}$ i.c.	[_separable]	✓

3458	$\frac{y^{'}}{\tan (x)} - \frac{y}{x^{2} + 1} = 0$	[_separable]	✓

3461	$2 x y^{'} + 3 x + y = 0$	[_linear]	✓

3467	$(y - x) y^{'} + 2 x + 3 y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3474	$y^{'} - \frac{y}{x} = 1$ i.c.	[_linear]	✓

3476	$y^{'} - \frac{y^{2}}{x^{2}} = \frac{1}{4}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

3477	$y^{'} - \frac{y^{2}}{x^{2}} = \frac{1}{4}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

3515	$y^{'} = 2 x y$	[_separable]	✓

3518	$y^{'} = \frac{y}{\ln (x) x}$	[_separable]	✓

3519	$y - (- 2 + x) y^{'} = 0$	[_separable]	✓

3541	$y^{'} - \frac{y}{x} = 2 x^{2} \ln (x)$	[_linear]	✓

3544	$(3 x - y) y^{'} = 3 y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3545	$y^{'} = \frac{{(x + y)}^{2}}{2 x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

3546	$\sin (\frac{y}{x}) (- y + x y^{'}) = x \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

3549	$x (x^{2} - y^{2}) - x (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

3551	$y^{'} = \frac{y^{2} + 2 x y - 2 x^{2}}{x^{2} - x y + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

3552	$2 x y y^{'} - 2 y^{2} - x^{2} e^{- \frac{y^{2}}{x^{2}}} = 0$	[[_homogeneous, ‘class A‘]]	✓

3553	$x^{2} y^{'} = y^{2} + 3 x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

3555	$2 x (2 x + y) y^{'} = y (4 x - y)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

3556	$x y^{'} = x \tan (\frac{y}{x}) + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

3562	$y^{'} = \frac{y}{2 x}$	[_separable]	✓

3593	$y^{'} = 2 x y$	[_separable]	✓

3596	$y^{'} = \frac{y}{\ln (x) x}$	[_separable]	✓

3597	$y - (- 1 + x) y^{'} = 0$	[_separable]	✓

3635	$- y + x y^{'} = x^{2} \ln (x)$	[_linear]	✓

3636	$y^{'} = \frac{y^{2} + x y + x^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

3637	$(3 x - y) y^{'} = 3 y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3638	$y^{'} = \frac{{(x + y)}^{2}}{2 x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

3639	$\sin (\frac{y}{x}) (- y + x y^{'}) = x \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

3642	$(x^{2} - y^{2}) y - x (x^{2} - y^{2}) y^{'} = 0$	[_separable]	✓

3644	$y^{'} = \frac{y^{2} + 2 x y - 2 x^{2}}{x^{2} - x y + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

3645	$2 x y y^{'} - 2 y^{2} - x^{2} e^{- \frac{y^{2}}{x^{2}}} = 0$	[[_homogeneous, ‘class A‘]]	✓

3646	$x^{2} y^{'} = y^{2} + 3 x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

3648	$2 x (2 x + y) y^{'} = y (4 x - y)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

3649	$x y^{'} = x \tan (\frac{y}{x}) + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

3651	$y^{'} = \frac{- 2 x + 4 y}{x + y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3652	$y^{'} = \frac{2 x - y}{x + 4 y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3655	$y^{'} = \frac{x + a y}{a x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3656	$y^{'} = \frac{x + \frac{y}{2}}{\frac{x}{2} - y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

3657	$y^{'} - \frac{y}{x} = \frac{4 x^{2} \cos (x)}{y}$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓

4097	$y^{'} = \frac{- 2 x + y}{x}$	[_linear]	✓

4098	$x^{3} + y^{3} - x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4099	$y^{'} + y = 0$	[_quadrature]	✓

4103	$y^{'} = \frac{x^{2} + y^{2}}{2 x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

4104	$x y^{'} = x + y$ i.c.	[_linear]	✓

4112	$y^{'} = \frac{2 x - y}{2 x + y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

4190	$y y^{'} = x$	[_separable]	✓

4196	$x y^{'} + y = x$	[_linear]	✓

4197	$- y + x y^{'} = x^{3}$	[_linear]	✓

4219	$x y^{'} = y$	[_separable]	✓

4220	$(1 - x) y^{'} = y$	[_separable]	✓

4221	$y^{'} = \frac{4 x y}{x^{2} + 1}$	[_separable]	✓

4222	$y^{'} = \frac{2 y}{x^{2} - 1}$	[_separable]	✓

4223	$x^{2} y^{'} - y^{2} = 0$ i.c.	[_separable]	✓

4224	$y^{'} + 2 x y = 0$ i.c.	[_separable]	✓

4225	$\cot (x) y^{'} = y$ i.c.	[_separable]	✓

4228	$x y^{'} = x y + y$ i.c.	[_separable]	✓

4233	$(1 - x) y^{'} = x y$	[_separable]	✓

4234	$(x^{2} - 1) y^{'} = (x^{2} + 1) y$	[_separable]	✓

4240	$x y y^{'} = 2 x^{2} - y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4241	$x^{2} - y^{2} + x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4242	$x^{2} y^{'} - 2 x y - 2 y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4243	$x^{2} y^{'} = 3 (x^{2} + y^{2}) \arctan (\frac{y}{x}) + x y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4244	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) + x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4245	$x y^{'} = y + 2 e^{- \frac{y}{x}}$	[[_homogeneous, ‘class D‘]]	✓

4254	$y + y \cos (x y) + (x + x \cos (x y)) y^{'} = 0$	[_separable]	✓

4257	$- \frac{\sin (\frac{x}{y})}{y} + \frac{x \sin (\frac{x}{y}) y^{'}}{y^{2}} = 0$	[_separable]	✓

4258	$1 + y + (1 - x) y^{'} = 0$	[_separable]	✓

4261	$(3 x^{2} - y^{2}) y^{'} - 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

4266	$x y^{'} = x^{5} + x^{3} y^{2} + y$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4267	$(x + y) y^{'} = y - x$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

4268	$x y^{'} = y + x^{2} + 9 y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4281	$(x y - x^{2}) y^{'} = y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

4283	$x^{2} + y = x y^{'}$	[_linear]	✓

4290	$y^{2} - 3 x y - 2 x^{2} = (x^{2} - x y) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

4295	$2 x y + x^{2} y^{'} = 0$	[_separable]	✓

4300	$\frac{x}{x^{2} + y^{2}} + \frac{y}{x^{2}} + (\frac{y}{x^{2} + y^{2}} - \frac{1}{x}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

4305	$y^{'} = \frac{x (1 + y^{2})}{y (x^{2} + 1)}$ i.c.	[_separable]	✓

4314	$y^{'} + \frac{x}{y} + 2 = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

4315	$- y + x y^{'} = x \cot (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4316	$x \cos {(\frac{y}{x})}^{2} - y + x y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4318	$x y + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

4319	$(1 - e^{- \frac{y}{x}}) y^{'} + 1 - \frac{y}{x} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4320	$x^{2} - x y + y^{2} - x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

4333	$2 x y + (x^{2} + 2 x y + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

4335	$y (2 x - y + 2) + 2 y^{'} (x - y) = 0$	[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

4346	$x^{2} + y + y^{2} - x y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4350	$y - 2 x^{3} \tan (\frac{y}{x}) - x y^{'} = 0$	[[_homogeneous, ‘class D‘]]	✓

4360	$(\sin {(y)}^{2} + x \cot (y)) y^{'} = 0$	[_quadrature]	✓

4398	$y^{'} = \frac{y + 2}{x + 1}$	[_separable]	✓

4399	$x y^{'} = y - e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4402	$y^{'} = e^{\frac{x y^{'}}{y}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4405	$- y + x y^{'} = x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4412	$x y + 2 x^{3} y + x^{2} y^{'} = 0$	[_separable]	✓

4422	$x - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4423	$x^{2} (- y + x y^{'}) = (x + y) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

4441	$x + \sin {(\frac{y}{x})}^{2} (y - x y^{'}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4618	$y^{'} = a x^{n} y$	[_separable]	✓

4621	$y^{'} = y \cot (x)$	[_separable]	✓

4624	$y^{'} = (2 \csc (2 x) + \cot (x)) y$	[_separable]	✓

4632	$y^{'} = y \sec (x)$	[_separable]	✓

4634	$y^{'} = y \tan (x)$	[_separable]	✓

4643	$y^{'} = (a + \cos (\ln (x)) + \sin (\ln (x))) y$	[_separable]	✓

4708	$y^{'} = \sqrt{X Y}$	[_quadrature]	✓

4743	$y + x + x y^{'} = 0$	[_linear]	✓

4744	$x y^{'} + x^{2} - y = 0$	[_linear]	✓

4746	$x y^{'} = 1 + x^{3} + y$	[_linear]	✓

4747	$x y^{'} = x^{m} + y$	[_linear]	✓

4749	$x y^{'} = x^{2} \sin (x) + y$	[_linear]	✓

4752	$x y^{'} = a y$	[_separable]	✓

4754	$x y^{'} = a x + b y$	[_linear]	✓

4759	$x y^{'} + (b x + a) y = 0$	[_separable]	✓

4760	$x y^{'} = x^{3} + (- 2 x^{2} + 1) y$	[_linear]	✓

4764	$x y^{'} = x^{2} + y (y + 1)$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4767	$x y^{'} = a x^{2} + y + b y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4773	$x y^{'} = (1 - x y) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

4774	$x y^{'} = (1 + x y) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

4776	$x y^{'} = x^{3} + (2 x^{2} + 1) y + x y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4777	$x y^{'} = y (2 x y + 1)$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

4786	$x y^{'} = y + (x^{2} - y^{2}) f (x)$	[[_homogeneous, ‘class D‘], _Riccati]	✓

4787	$x y^{'} = y (1 + y^{2})$	[_separable]	✓

4800	$x y^{'} + x - y + x \cos (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4801	$x y^{'} = y - x \cos {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4805	$x y^{'} - y + x \sec (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4806	$x y^{'} = y + x \sec {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4808	$x y^{'} = y + x \sin (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4811	$x y^{'} = y - x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4813	$x y^{'} = e^{\frac{y}{x}} x + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4814	$x y^{'} = x + y + e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4818	$x y^{'} = y - 2 x \tanh (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

4850	$x^{2} y^{'} = a + b x + c x^{2} + x y$	[_linear]	✓

4854	$x^{2} y^{'} = (b x + a) y$	[_separable]	✓

4857	$x^{2} y^{'} + x^{2} + x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

4860	$x^{2} y^{'} = (x + a y) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4861	$x^{2} y^{'} = (a x + b y) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4862	$x^{2} y^{'} + a x^{2} + b x y + c y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

4870	$x^{2} y^{'} + (x^{2} + y^{2} - x) y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

4879	$(- x^{2} + 1) y^{'} = 5 - x y$	[_linear]	✓

4881	$y^{'} (x^{2} + 1) + a - x y = 0$	[_linear]	✓

4888	$(- x^{2} + 1) y^{'} + 2 x y = 0$	[_separable]	✓

4894	$y^{'} (x^{2} + 1) = (2 b x + a) y$	[_separable]	✓

4905	$(a^{2} + x^{2}) y^{'} = b + x y$	[_linear]	✓

4913	$x (x + 1) y^{'} = (1 - 2 x) y$	[_separable]	✓

4922	$(x - a) (x - b) y^{'} + k y = 0$	[_separable]	✓

4927	$2 x^{2} y^{'} = y$	[_separable]	✓

4930	$2 x^{2} y^{'} = 2 x y + (1 - x \cot (x)) (x^{2} - y^{2})$	[[_homogeneous, ‘class D‘], _Riccati]	✓

4938	$a x^{2} y^{'} = x^{2} + y a x + b^{2} y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

4944	$x^{3} y^{'} = 3 - x^{2} + x^{2} y$	[_linear]	✓

4946	$x^{3} y^{'} = y (x^{2} + y)$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

4947	$x^{3} y^{'} = x^{2} (y - 1) + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4951	$x^{3} y^{'} = (2 x^{2} + y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4955	$x (x^{2} + 1) y^{'} = a x^{3} + y$	[_linear]	✓

4957	$x (x^{2} + 1) y^{'} = (- x^{2} + 1) y$	[_separable]	✓

4958	$x (- x^{2} + 1) y^{'} = (x^{2} - x + 1) y$	[_separable]	✓

4959	$x (- x^{2} + 1) y^{'} = a x^{3} + (- 2 x^{2} + 1) y$	[_linear]	✓

4964	$x^{2} (1 - x) y^{'} = (2 - x) x y - y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

4965	$2 x^{3} y^{'} = (x^{2} - y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4966	$2 x^{3} y^{'} = (3 x^{2} + a y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

4968	$x (c x^{2} + b x + a) y^{'} + x^{2} - (c x^{2} + b x + a) y = y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4969	$x^{4} y^{'} = (x^{3} + y) y$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

4976	$x (- 2 x^{3} + 1) y^{'} = 2 (- x^{3} + 1) y$	[_separable]	✓

4979	$x (- x^{4} + 1) y^{'} = 2 x (x^{2} - y^{2}) + (- x^{4} + 1) y$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

4995	$y^{'} \sqrt{X} + \sqrt{Y} = 0$	[_quadrature]	✓

4996	$y^{'} \sqrt{X} = \sqrt{Y}$	[_quadrature]	✓

5002	$y^{'} \sqrt{X} = 0$	[_quadrature]	✓

5003	$y^{'} \sqrt{X} + \sqrt{Y} = 0$	[_quadrature]	✓

5004	$y^{'} \sqrt{X} = \sqrt{Y}$	[_quadrature]	✓

5007	$X^{2 / 3} y^{'} = Y^{2 / 3}$	[_quadrature]	✓

5009	$(1 - 4 \cos {(x)}^{2}) y^{'} = \tan (x) (1 + 4 \cos {(x)}^{2}) y$	[_separable]	✓

5010	$(1 - \sin (x)) y^{'} + y \cos (x) = 0$	[_separable]	✓

5011	$(\cos (x) - \sin (x)) y^{'} + y (\cos (x) + \sin (x)) = 0$	[_separable]	✓

5014	$y^{'} x \ln (x) = a x (1 + \ln (x)) - y$	[_linear]	✓

5015	$x + y y^{'} = 0$	[_separable]	✓

5018	$y y^{'} + a x + b y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5021	$y y^{'} + 4 x (x + 1) + y^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5032	$(x + y) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5033	$y^{'} (x - y) = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5034	$(x + y) y^{'} + x - y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5035	$(x + y) y^{'} = x - y$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5037	$y^{'} (x - y) = y (2 x y + 1)$	[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5039	$y^{'} (x - y) = (e^{- \frac{x}{y}} + 1) y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5044	$(2 x + y) y^{'} + x - 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5051	$(4 x - y) y^{'} + 2 x - 5 y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5058	$2 y y^{'} + 2 x + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5060	$(x - 2 y) y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5061	$(x + 2 y) y^{'} + 2 x - y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5062	$(x - 2 y) y^{'} + 2 x + y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5081	$(x + 4 y) y^{'} + 4 x - y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5088	$(7 x + 5 y) y^{'} + 10 x + 8 y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5097	$(a x + b y) y^{'} + x = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

5098	$(a x + b y) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5099	$(a x + b y) y^{'} + b x + a y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5100	$(a x + b y) y^{'} = b x + a y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5102	$x y y^{'} = x + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5103	$x y y^{'} + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5104	$x y y^{'} + x^{4} - y^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5105	$x y y^{'} = a x^{3} \cos (x) + y^{2}$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓

5106	$x y y^{'} = x^{2} - x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5107	$x y y^{'} + 2 x^{2} - 2 x y - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5111	$x y y^{'} + x^{2} arccot (\frac{y}{x}) - y^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5112	$x y y^{'} + x^{2} e^{- \frac{2 y}{x}} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5122	$x (x + y) y^{'} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5123	$x (x - y) y^{'} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5124	$x (x + y) y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5125	$x (x - y) y^{'} + 2 x^{2} + 3 x y - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5128	$x (2 x + y) y^{'} = x^{2} + x y - y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5129	$x (4 x - y) y^{'} + 4 x^{2} - 6 x y - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5134	$(x + a) (x + b) y^{'} = x y$	[_separable]	✓

5138	$2 x y y^{'} + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓

5139	$2 x y y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5143	$x (x - 2 y) y^{'} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5144	$x (x + 2 y) y^{'} + (2 x - y) y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5145	$x (x - 2 y) y^{'} + (2 x - y) y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5150	$x (2 x + 3 y) y^{'} = y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5151	$x (2 x + 3 y) y^{'} + 3 {(x + y)}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5154	$a x y y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5155	$a x y y^{'} + x^{2} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5157	$x (x - a y) y^{'} = y (y - a x)$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5167	$(x^{2} + 1) y y^{'} + x (1 - y^{2}) = 0$	[_separable]	✓

5169	$2 x^{2} y y^{'} = x^{2} (2 x + 1) - y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5173	$x^{2} (x - 2 y) y^{'} = 2 x^{3} - 4 x y^{2} + y^{3}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

5176	$x^{2} (4 x - 3 y) y^{'} = (6 x^{2} - 3 x y + 2 y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

5181	$8 x^{3} y y^{'} + 3 x^{4} - 6 y^{2} x^{2} - y^{4} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5192	$x y + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5193	$(x^{2} + y^{2}) y^{'} = x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5194	$(x^{2} - y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5195	$(x^{2} - y^{2}) y^{'} + x (x + 2 y) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5196	$(x^{2} + y^{2}) y^{'} + 2 x (2 x + y) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5201	$(3 x^{2} - y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5210	$(x^{2} + 2 x y - y^{2}) y^{'} + x^{2} - 2 x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5211	${(x + y)}^{2} y^{'} = x^{2} - 2 x y + 5 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5213	$(2 x^{2} + 4 x y - y^{2}) y^{'} = x^{2} - 4 x y - 2 y^{2}$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5214	${(3 x + y)}^{2} y^{'} = 4 (3 x + 2 y) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5219	$(2 x^{2} + 3 y^{2}) y^{'} + x (3 x + y) = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5221	$(3 x^{2} + 2 x y + 4 y^{2}) y^{'} + 2 x^{2} + 6 x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5225	$(x^{2} + a y^{2}) y^{'} = x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5226	$(x^{2} + x y + a y^{2}) y^{'} = a x^{2} + x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5227	$(a x^{2} + 2 x y - a y^{2}) y^{'} + x^{2} - 2 y a x - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5228	$(a x^{2} + 2 b x y + c y^{2}) y^{'} + k x^{2} + 2 y a x + b y^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5231	$x (x^{2} + y^{2}) y^{'} = (x^{2} + x^{4} + y^{2}) y$	[[_homogeneous, ‘class D‘], _rational]	✓

5234	$x (2 x^{2} + y^{2}) y^{'} = (2 x^{2} + 3 y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5237	$x (x^{2} - x y + y^{2}) y^{'} + (y^{2} + x y + x^{2}) y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5238	$x (x^{2} - x y - y^{2}) y^{'} = (x^{2} + x y - y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5239	$x (x^{2} + y a x + y^{2}) y^{'} = (x^{2} + b x y + y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5240	$x (x^{2} - 2 y^{2}) y^{'} = (2 x^{2} - y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5241	$x (x^{2} + 2 y^{2}) y^{'} = (2 x^{2} + 3 y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5242	$2 x (5 x^{2} + y^{2}) y^{'} = x^{2} y - y^{3}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5243	$x (x^{2} + y a x + 2 y^{2}) y^{'} = (a x + 2 y) y^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5251	$x (x^{2} - 6 y^{2}) y^{'} = 4 (x^{2} + 3 y^{2}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5267	$(x^{3} - y^{3}) y^{'} + x^{2} y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5268	$(x^{3} + y^{3}) y^{'} + x^{2} (a x + 3 y) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5272	$(3 x^{2} + y^{2}) y y^{'} + x (x^{2} + 3 y^{2}) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5274	$2 y^{3} y^{'} = x^{3} - x y^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5276	$(3 x^{2} + 2 y^{2}) y y^{'} + x^{3} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5277	$(5 x^{2} + 2 y^{2}) y y^{'} + x (x^{2} + 5 y^{2}) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5279	$(3 x^{3} + 6 x^{2} y - 3 x y^{2} + 20 y^{3}) y^{'} + 4 x^{3} + 9 x^{2} y + 6 x y^{2} - y^{3} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5280	$(x^{3} + a y^{3}) y^{'} = x^{2} y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5283	$x (2 x^{3} + y^{3}) y^{'} = (2 x^{3} - x^{2} y + y^{3}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5284	$x (2 x^{3} - y^{3}) y^{'} = (x^{3} - 2 y^{3}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5285	$x (x^{3} + 3 x^{2} y + y^{3}) y^{'} = (3 x^{2} + y^{2}) y^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5286	$x (x^{3} - 2 y^{3}) y^{'} = (2 x^{3} - y^{3}) y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5301	$(a x^{3} + {(a x + b y)}^{3}) y y^{'} + x ({(a x + b y)}^{3} + b y^{3}) = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5328	$x (x - y \tan (\frac{y}{x})) y^{'} + (x + y \tan (\frac{y}{x})) y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5685	$y \ln (y^{'}) + y^{'} - y \ln (y) - x y = 0$	[_separable]	✓

5689	$y^{'} = \frac{x y}{x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5694	$\frac{2 x}{y^{3}} + \frac{(y^{2} - 3 x^{2}) y^{'}}{y^{4}} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5695	$y + x y^{2} - x y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5705	$(y - x) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5708	$x - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5709	$(7 x + 5 y) y^{'} + 10 x + 8 y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5713	$x (- x^{2} + 1) y^{'} + (2 x^{2} - 1) y = a x^{3}$	[_linear]	✓

5734	$(7 x + 5 y) y^{'} + 10 x + 8 y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5735	$x^{2} + 2 x y - y^{2} + (y^{2} + 2 x y - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5736	$y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5763	$y = x y^{'} + x \sqrt{1 + {y^{'}}^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5771	$2 x y + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5773	$x + y - y^{'} (x - y) = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

5774	$x y^{'} - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5775	$2 x^{2} y + y^{3} + (x y^{2} - 2 x^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5777	$\frac{y \cos (\frac{y}{x})}{x} - (\frac{x \sin (\frac{y}{x})}{y} + \cos (\frac{y}{x})) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5778	$y + x \ln (\frac{y}{x}) y^{'} - 2 x y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5779	$2 y e^{\frac{x}{y}} + (y - 2 x e^{\frac{x}{y}}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5780	$e^{\frac{y}{x}} x - y \sin (\frac{y}{x}) + x \sin (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5781	$x^{2} + y^{2} = 2 x y y^{'}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5782	$e^{\frac{y}{x}} x + y = x y^{'}$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5783	$y^{'} - \frac{y}{x} + \csc (\frac{y}{x}) = 0$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5784	$x y - y^{2} - x^{2} y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5787	$x + y + 1 + (2 x + 2 y + 2) y^{'} = 0$	[_quadrature]	✓

5854	$- y + x y^{'} = x^{2} \sin (x)$	[_linear]	✓

5855	$x y^{'} + x y^{2} - y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5857	$x^{2} (- 1 + x) y^{'} - y^{2} - x (- 2 + x) y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5865	$y^{'} = 1 + \frac{y}{x} - \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

5874	$(x^{2} - y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5880	$2 y - x y \ln (x) - 2 y^{'} x \ln (x) = 0$	[_separable]	✓

5888	$x y^{'} = x + y + e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5891	$x^{3} y^{'} - y^{2} - x^{2} y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

5893	$x y^{'} - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

5894	$(x y - x^{2}) y^{'} + y^{2} - 3 x y - 2 x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

5896	$x^{2} y^{'} + x^{2} + x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

5906	$x y y^{'} + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5907	$2 x y y^{'} + 3 x^{2} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

5908	$(2 x y^{3} - x^{4}) y^{'} + 2 x^{3} y - y^{4} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

5910	$(x^{2} + y^{2}) y^{'} + 2 x (2 x + y) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

5912	$2 y^{3} y^{'} + x y^{2} - x^{3} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

6025	$y^{'} + y \tan (x) = 0$	[_separable]	✓

6092	$y^{'} = y$	[_quadrature]	✓

6093	$x y^{'} = y$ i.c.	[_separable]	✓

6125	$x^{2} y^{'} + y^{2} - x y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

6127	$x y + (y^{2} - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

6128	$y^{2} - x y + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

6130	$y^{'} = \frac{y}{x} - \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

6133	$y^{'} = \frac{2 y^{2}}{x} + \frac{y}{x} - 2 x$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

6208	$x^{2} y^{'} - x y = \frac{1}{x}$	[_linear]	✓

6218	$y + 2 x - x y^{'} = 0$	[_linear]	✓

6224	$(2 x + y) y^{'} - x + 2 y = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

6226	$\sin {(x)}^{2} y^{'} + \sin {(x)}^{2} + (x + y) \sin (2 x) = 0$	[_linear]	✓

6232	$3 x^{2} y + x^{3} y^{'} = 0$ i.c.	[_separable]	✓

6233	$- y + x y^{'} = x^{2}$ i.c.	[_linear]	✓

6237	$x y^{'} = x y + y$	[_separable]	✓

6239	$y^{'} = 3 x^{2} y$	[_separable]	✓

6241	$x y^{'} = y$	[_separable]	✓

6263	$x^{'} = 3 x t^{2}$	[_separable]	✓

6285	$y^{'} = 2 y - 2 t y$ i.c.	[_separable]	✓

6296	$(t^{2} + 1) y^{'} = t y - y$	[_separable]	✓

6301	$y^{'} = \frac{y}{x} + 2 x + 1$	[_linear]	✓

6310	$y^{'} - \frac{y}{x} = x e^{x}$ i.c.	[_linear]	✓

6322	$x^{2} y + x^{4} \cos (x) - x^{3} y^{'} = 0$	[_linear]	✓

6404	$y^{'} (x^{2} + 1) = 1 + x y$	[_linear]	✓

6421	$- y + x y^{'} = x^{2}$	[_linear]	✓

6424	$(x^{3} + x y^{2}) y^{'} = 2 y^{3}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

6431	$(x^{3} + 1) y^{'} = x^{2} y$ i.c.	[_separable]	✓

6435	$(- x + 2 y) y^{'} = 2 x + y$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

6436	$x y + y^{2} + (x^{2} - x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

6437	$x^{3} + y^{3} = 3 x y^{2} y^{'}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

6438	$y - 3 x + (4 y + 3 x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

6439	$(x^{3} + 3 x y^{2}) y^{'} = 3 x^{2} y + y^{3}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

6457	$x^{2} - 2 x y + 5 y^{2} = (x^{2} + 2 x y + y^{2}) y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

6459	$y + (x^{2} - 4 x) y^{'} = 0$	[_separable]	✓

6461	$y^{'} = \frac{2 x y + y^{2}}{x^{2} + 2 x y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

6464	$x^{2} y^{'} = y^{2} - x y y^{'}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

6467	$y^{2} + x^{2} y^{'} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

6468	$2 x y y^{'} = x^{2} - y^{2}$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓

6475	$x (1 + y^{2}) - (x^{2} + 1) y y^{'} = 0$	[_separable]	✓

6542	$y^{'} - \frac{y}{x} = x^{2}$	[_linear]	✓

6569	$x y^{'} = 2 y$	[_separable]	✓

6570	$x + y y^{'} = 0$	[_separable]	✓

6572	$2 x^{3} y^{'} = y (3 x^{2} + y^{2})$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

6579	$4 y + x y^{'} = 0$	[_separable]	✓

6581	$y^{2} - x^{2} y^{'} = 0$	[_separable]	✓

6582	$1 + y - (x + 1) y^{'} = 0$	[_separable]	✓

6584	$x \sin (\frac{y}{x}) - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

6585	$y^{2} (x^{2} + 2) + (x^{3} + y^{3}) (y - x y^{'}) = 0$	[[_homogeneous, ‘class D‘], _rational]	✓

6589	$x y + y^{'} (x^{2} + 1) = 0$	[_separable]	✓

6590	$x + 2 y + (2 x + 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

6594	$y^{2} - x^{2} + x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

6597	$x^{3} + y^{3} + 3 x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓

6599	$x y^{'} + 2 y = 0$ i.c.	[_separable]	✓

6600	$x y y^{'} + x^{2} + y^{2} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

6615	$y (x - 2 y) - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

6616	$x y y^{'} + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

6617	$2 x y y^{'} + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓

6641	$y^{'} + y = 2 + 2 x$	[[_linear, ‘class A‘]]	✓

6642	$y^{'} - y = x y$	[_separable]	✓

6886	$2 y^{'} + y = 0$	[_quadrature]	✓

6890	$(y - x) y^{'} = y - x$	[_quadrature]	✓

6904	$x y^{'} - 2 y = 0$	[_separable]	✓

6905	$y^{'} = - \frac{x}{y}$	[_separable]	✓

6906	$y^{'} + 2 y = 0$	[_quadrature]	✓

6907	$5 y^{'} = 2 y$	[_quadrature]	✓

6948	$x y^{'} = 2 y$ i.c.	[_separable]	✓

6951	$x y^{'} = y$	[_separable]	✓

6955	$(x^{2} + y^{2}) y^{'} = y^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

6956	$(y - x) y^{'} = x + y$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

6961	$x y^{'} = y$ i.c.	[_separable]	✓

6968	$y y^{'} = 3 x$ i.c.	[_separable]	✓

6969	$y y^{'} = 3 x$ i.c.	[_separable]	✓

6970	$y y^{'} = 3 x$ i.c.	[_separable]	✓

6982	$x y^{'} = 2 x$	[_quadrature]	✓

6983	$y^{'} = 2$	[_quadrature]	✓

6985	$x y^{'} = y$	[_separable]	✓

6990	$3 x y^{'} - 2 y = 0$	[_separable]	✓

6992	$x y^{'} + y = 2 x$ i.c.	[_linear]	✓

7034	$y y^{'} = - x$ i.c.	[_separable]	✓

7035	$y y^{'} = - x$ i.c.	[_separable]	✓

7044	$y^{'} = 1 - \frac{y}{x}$ i.c.	[_linear]	✓

7045	$y^{'} = 1 - \frac{y}{x}$ i.c.	[_linear]	✓

7067	$x y^{'} = 4 y$	[_separable]	✓

7077	$s^{'} = k s$	[_quadrature]	✓

7080	$n^{'} + n = n t e^{t + 2}$	[_separable]	✓

7087	$x^{2} y^{'} = y - x y$ i.c.	[_separable]	✓

7093	$y^{'} = y e^{- x^{2}}$ i.c.	[_separable]	✓

7127	$y^{'} = - \frac{x}{y}$ i.c.	[_separable]	✓

7130	$y^{'} = y$ i.c.	[_quadrature]	✓

7131	$y^{'} = y + \frac{y}{\ln (x) x}$ i.c.	[_separable]	✓

7145	$y^{'} = 5 y$	[_quadrature]	✓

7146	$y^{'} + 2 y = 0$	[_quadrature]	✓

7153	$- y + x y^{'} = x^{2} \sin (x)$	[_linear]	✓

7192	$y^{'} - \sin (x^{2}) y = 0$ i.c.	[_separable]	✓

7199	$e^{'} = - \frac{e}{r c}$ i.c.	[_quadrature]	✓

7384	$y^{'} = y \sin (x)$	[_separable]	✓

7396	$\frac{y}{- 1 + x} + \frac{x y^{'}}{y + 1} = 0$	[_separable]	✓

7417	$x - y + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7418	$y - 2 x y + x^{2} y^{'} = 0$	[_separable]	✓

7420	$y^{2} + x^{2} y^{'} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

7421	$(x^{2} + y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

7422	$- y + x y^{'} = x \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7423	$x y^{'} = y - e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7424	$- y + x y^{'} = (x + y) \ln (\frac{x + y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7425	$x y^{'} = y \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7428	$x + y - y^{'} (x - y) = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7429	$x^{2} + 2 x y - y^{2} + (y^{2} + 2 x y - x^{2}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

7430	$- y + x y^{'} = y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7431	$y^{2} + (x^{2} - x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

7432	$y^{2} + x y + x^{2} = x^{2} y^{'}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

7433	$\frac{1}{x^{2} - x y + y^{2}} = \frac{y^{'}}{2 y^{2} - x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

7434	$y^{'} = \frac{2 x y}{3 x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

7435	$y^{'} = \frac{x}{y} + \frac{y}{x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7438	$x y^{'} = y \ln (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7444	$y^{'} + \frac{x + 2 y}{x} = 0$	[_linear]	✓

7445	$y^{'} = \frac{y}{x + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7477	$2 x + 4 y + (2 x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7509	$x^{2} y^{'} + y^{2} - x y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7510	$x + y - y^{'} (x - y) = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7549	$\frac{1}{y} + \sec (\frac{y}{x}) - \frac{x y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class D‘]]	✓

7555	$y e^{x y} + x e^{x y} y^{'} = 0$	[_separable]	✓

7560	$x^{2} + y^{2} - 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7561	$x^{2} - y^{2} + 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7562	$- y + x y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

7564	$x + y y^{'} + y - x y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7583	$y^{'} + \cos (x) y = 0$	[_separable]	✓

7590	$y^{'} = k y$	[_quadrature]	✓

7731	$y^{'} = x^{2} y$	[_separable]	✓

7732	$y y^{'} = x$	[_separable]	✓

7739	$y^{'} = \frac{x + y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7740	$y^{'} = \frac{y^{2}}{x^{2} + x y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

7741	$y^{'} = \frac{y^{2} + x y + x^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

7742	$y^{'} = \frac{y + x e^{- \frac{2 y}{x}}}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7774	$x y^{'} = 2 y$	[_separable]	✓

7776	$y^{'} = k y$	[_quadrature]	✓

7780	$x y^{'} = y + x^{2} + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

7781	$y^{'} = \frac{x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

7782	$2 x y y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7784	$y^{'} = \frac{y^{2}}{x y - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

7807	$x^{5} y^{'} + y^{5} = 0$	[_separable]	✓

7808	$y^{'} = 4 x y$	[_separable]	✓

7809	$y^{'} + y \tan (x) = 0$	[_separable]	✓

7814	$y^{'} - y \tan (x) = 0$	[_separable]	✓

7848	$x y^{'} = 2 x^{2} y + y \ln (x)$	[_separable]	✓

7854	$y + y \cos (x y) + (x + x \cos (x y)) y^{'} = 0$	[_separable]	✓

7858	$1 + y + (1 - x) y^{'} = 0$	[_separable]	✓

7871	$x^{2} - 2 y^{2} + x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7872	$x^{2} y^{'} - 3 x y - 2 y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7873	$x^{2} y^{'} = 3 (x^{2} + y^{2}) \arctan (\frac{y}{x}) + x y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7874	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) + x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7875	$x y^{'} = y + 2 x e^{- \frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7876	$x - y - (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7877	$x y^{'} = 2 x - 6 y$	[_linear]	✓

7879	$x^{2} y^{'} = 2 x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7880	$x^{3} + y^{3} - x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

7889	$y^{'} = \sin (\frac{y}{x}) - \cos (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7890	$e^{\frac{x}{y}} - \frac{y y^{'}}{x} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7891	$y^{'} = \frac{x^{2} - x y}{y^{2} \cos (\frac{x}{y})}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7892	$y^{'} = \frac{y \tan (\frac{y}{x})}{x}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

7917	$x y^{'} + y = x$	[_linear]	✓

7919	$x^{2} y^{'} = y$	[_separable]	✓

7921	$y^{'} = \frac{x^{2} + y^{2}}{x^{2} - y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

7922	$y^{'} = \frac{x + 2 y}{2 x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7923	$2 x y + x^{2} y^{'} = 0$	[_separable]	✓

7925	$- y + x y^{'} = 2 x$ i.c.	[_linear]	✓

7929	$y^{'} = \frac{x + y}{x - y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

7930	$y^{'} = \frac{x^{2} + 2 y^{2}}{x^{2} - 2 y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

7932	$\frac{1}{y} - \frac{x y^{'}}{y^{2}} = 0$	[_separable]	✓

8073	$y^{'} = 2 x y$	[_separable]	✓

8079	$y^{'} + y = 0$	[_quadrature]	✓

8081	$y^{'} - y = 0$	[_quadrature]	✓

8085	$x y^{'} = y$	[_separable]	✓

8087	$x^{2} y^{'} = y$	[_separable]	✓

8089	$y^{'} - \frac{y}{x} = x^{2}$	[_linear]	✓

8697	$y^{'} = \frac{y}{\ln (x) x}$	[_separable]	✓

8701	$y^{'} = \frac{2 x - y}{x + 4 y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

8720	$y^{'} = y$	[_quadrature]	✓

8721	$y^{'} = 0$	[_quadrature]	✓

8724	$y^{'} = \frac{2 y}{x}$ i.c.	[_separable]	✓

8725	$y^{'} = \frac{2 y}{x}$	[_separable]	✓

8734	$y^{2} + x^{2} y^{'} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

8736	$(x + y) y^{'} = 0$	[_quadrature]	✓

8737	$x y^{'} = 0$	[_quadrature]	✓

8738	$\frac{y^{'}}{x + y} = 0$	[_quadrature]	✓

8739	$\frac{y^{'}}{x} = 0$	[_quadrature]	✓

8740	$y^{'} = 0$	[_quadrature]	✓

8742	$y^{'} = \frac{5 x^{2} - x y + y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

8751	$y y^{'} - y = x$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

8792	$y^{'} = \frac{y (1 + \frac{a^{2} x}{\sqrt{a^{2} (x^{2} + 1)}})}{\sqrt{a^{2} (x^{2} + 1)}}$	[_separable]	✓

8886	$y^{'} = e^{- \frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

8887	$y^{'} = 2 x^{2} \sin {(\frac{y}{x})}^{2} + \frac{y}{x}$	[[_homogeneous, ‘class D‘]]	✓

8985	$y^{'} = 0$	[_quadrature]	✓

8986	$y^{'} = a$	[_quadrature]	✓

8988	$y^{'} = 1$	[_quadrature]	✓

8990	$y^{'} = y a x$	[_separable]	✓

8993	$y^{'} = y$	[_quadrature]	✓

8994	$y^{'} = b y$	[_quadrature]	✓

8996	$c y^{'} = 0$	[_quadrature]	✓

8997	$c y^{'} = a$	[_quadrature]	✓

9001	$c y^{'} = y$	[_quadrature]	✓

9002	$c y^{'} = b y$	[_quadrature]	✓

9008	$a \sin (x) y x y^{'} = 0$	[_quadrature]	✓

9009	$f (x) \sin (x) y x y^{'} π = 0$	[_quadrature]	✓

9012	$y^{'} = \cos (x) + \frac{y}{x}$	[_linear]	✓

9015	$x y^{'} = 0$	[_quadrature]	✓

9016	$5 y^{'} = 0$	[_quadrature]	✓

9017	$e y^{'} = 0$	[_quadrature]	✓

9018	$π y^{'} = 0$	[_quadrature]	✓

9019	$\sin (x) y^{'} = 0$	[_quadrature]	✓

9020	$f (x) y^{'} = 0$	[_quadrature]	✓

9023	$(- 1 + x) y^{'} = 0$	[_quadrature]	✓

9024	$y y^{'} = 0$	[_quadrature]	✓

9025	$x y y^{'} = 0$	[_quadrature]	✓

9026	$x y \sin (x) y^{'} = 0$	[_quadrature]	✓

9027	$π y \sin (x) y^{'} = 0$	[_quadrature]	✓

9028	$x \sin (x) y^{'} = 0$	[_quadrature]	✓

9031	${y^{'}}^{n} = 0$	[_quadrature]	✓

9032	$x {y^{'}}^{n} = 0$	[_quadrature]	✓

10023	$y^{'} - (a + \cos (\ln (x)) + \sin (\ln (x))) y = 0$	[_separable]	✓

10103	$x y^{'} - y - \frac{x}{\ln (x)} = 0$	[_linear]	✓

10104	$x y^{'} - y - x^{2} \sin (x) = 0$	[_linear]	✓

10105	$x y^{'} - y - \frac{x \cos (\ln (\ln (x)))}{\ln (x)} = 0$	[_linear]	✓

10109	$x y^{'} + a y^{2} - y + b x^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

10113	$x y^{'} + x y^{2} - y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

10114	$x y^{'} + x y^{2} - y - a x^{3} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

10115	$x y^{'} + x y^{2} - (2 x^{2} + 1) y - x^{3} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

10122	$x y^{'} + f (x) (y^{2} - x^{2}) - y = 0$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10128	$x y^{'} - e^{\frac{y}{x}} x - y - x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10134	$x y^{'} - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10135	$x y^{'} + x - y + x \cos (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10136	$x y^{'} + x \tan (\frac{y}{x}) - y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10146	$x^{2} y^{'} - (- 1 + x) y = 0$	[_separable]	✓

10147	$x^{2} y^{'} + x^{2} + x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

10148	$x^{2} y^{'} - y^{2} - x y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

10149	$x^{2} y^{'} - y^{2} - x y - x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

10164	$(x^{2} - 1) y^{'} - x y + a = 0$	[_linear]	✓

10178	$3 x^{2} y^{'} - 7 y^{2} - 3 x y - x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

10182	$x^{3} y^{'} - y^{2} - x^{2} y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

10185	$x (x^{2} + 1) y^{'} + x^{2} y = 0$	[_separable]	✓

10186	$x (x^{2} - 1) y^{'} - (2 x^{2} - 1) y + a x^{3} = 0$	[_linear]	✓

10188	$x^{2} (- 1 + x) y^{'} - y^{2} - x (- 2 + x) y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

10191	$(a x^{2} + b x + c) (- y + x y^{'}) - y^{2} + x^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

10194	$(2 x^{4} - x) y^{'} - 2 (x^{3} - 1) y = 0$	[_separable]	✓

10204	$y^{'} x \ln (x) + y - a x (1 + \ln (x)) = 0$	[_linear]	✓

10214	$y y^{'} + a y + x = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

10217	$y y^{'} + y^{2} + 4 x (x + 1) = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

10221	$y y^{'} - x e^{\frac{x}{y}} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10232	$(- x + 2 y) y^{'} - y - 2 x = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

10241	$x y y^{'} + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

10242	$x y y^{'} - y^{2} + a x^{3} \cos (x) = 0$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓

10248	$(x y - x^{2}) y^{'} + y^{2} - 3 x y - 2 x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

10250	$2 x y y^{'} - y^{2} + a x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

10255	$x (2 x + 3 y) y^{'} + 3 {(x + y)}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

10267	$2 x^{2} y y^{'} + y^{2} - 2 x^{3} - x^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

10271	$(2 x^{2} y - x^{3}) y^{'} + y^{3} - 4 x y^{2} + 2 x^{3} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

10279	$(x^{2} + y^{2}) y^{'} + 2 x (2 x + y) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

10280	$(x^{2} + y^{2}) y^{'} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10284	$(y^{2} - x^{2}) y^{'} + 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10289	$x^{2} + 2 x y - y^{2} + (y^{2} + 2 x y - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10292	$(4 y^{2} + x^{2}) y^{'} - x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10293	$(3 x^{2} + 2 x y + 4 y^{2}) y^{'} + 2 x^{2} + 6 x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

10298	$(a y^{2} + 2 b x y + c x^{2}) y^{'} + b y^{2} + 2 c x y + d x^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

10303	$x (y^{2} + x y - x^{2}) y^{'} - y^{3} + x y^{2} + x^{2} y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10305	$2 x (5 x^{2} + y^{2}) y^{'} + y^{3} - x^{2} y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10314	$(y^{3} - x^{3}) y^{'} - x^{2} y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10316	$2 y^{3} y^{'} + x y^{2} = 0$	[_separable]	✓

10318	$(2 y^{3} + 5 x^{2} y) y^{'} + 5 x y^{2} + x^{3} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

10319	$(3 x^{3} + 6 x^{2} y - 3 x y^{2} + 20 y^{3}) y^{'} + 4 x^{3} + 9 x^{2} y + 6 x y^{2} - y^{3} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

10323	$(2 x y^{3} - x^{4}) y^{'} + 2 x^{3} y - y^{4} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10333	$y (y^{3} - 2 x^{3}) y^{'} + (2 y^{3} - x^{3}) x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10334	$y ({(b x + a y)}^{3} + b x^{3}) y^{'} + x ({(b x + a y)}^{3} + a y^{3}) = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

10356	$x y^{'} \cot (\frac{y}{x}) + 2 x \sin (\frac{y}{x}) - y \cot (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘]]	✓

10370	$(- y + x y^{'}) \cos {(\frac{y}{x})}^{2} + x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10371	$(y \sin (\frac{y}{x}) - x \cos (\frac{y}{x})) x y^{'} - (x \cos (\frac{y}{x}) + y \sin (\frac{y}{x})) y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

10437	$y^{'} - 1 = 0$	[_quadrature]	✓

10558	$x (\sqrt{1 + {y^{'}}^{2}} + y^{'}) - y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

10566	$y \ln (y^{'}) + y^{'} - y \ln (y) - x y = 0$	[_separable]	✓

10596	$y^{'} = \frac{y + F (\frac{y}{x})}{- 1 + x}$	[[_homogeneous, ‘class D‘]]	✓

10608	$y^{'} = \frac{y + F (\frac{y}{x}) x^{2}}{x}$	[[_homogeneous, ‘class D‘]]	✓

10673	$y^{'} = \frac{y + x^{3} a e^{x} + a x^{4} + a x^{3} - x y^{2} e^{x} - y^{2} x^{2} - x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10675	$y^{'} = \frac{y + x^{3} a \ln (x + 1) + a x^{4} + a x^{3} - x y^{2} \ln (x + 1) - y^{2} x^{2} - x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10677	$y^{'} = \frac{y + x^{3} \ln (x) + x^{4} + x^{3} + 7 x y^{2} \ln (x) + 7 y^{2} x^{2} + 7 x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10679	$y^{'} = \frac{y + x^{3} b \ln (\frac{1}{x}) + x^{4} b + b x^{3} + x a y^{2} \ln (\frac{1}{x}) + a x^{2} y^{2} + a x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10683	$y^{'} = \frac{y + \ln ((- 1 + x) (x + 1)) x^{3} + 7 \ln ((- 1 + x) (x + 1)) x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10685	$y^{'} = \frac{y - \ln (\frac{x + 1}{- 1 + x}) x^{3} + \ln (\frac{x + 1}{- 1 + x}) x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10686	$y^{'} = \frac{y + e^{\frac{x + 1}{- 1 + x}} x^{3} + e^{\frac{x + 1}{- 1 + x}} x y^{2}}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10687	$y^{'} = \frac{x y - y - e^{x + 1} x^{3} + e^{x + 1} x y^{2}}{(- 1 + x) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10693	$y^{'} = \frac{y \ln (- 1 + x) + x^{4} + x^{3} + y^{2} x^{2} + x y^{2}}{\ln (- 1 + x) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10694	$y^{'} = \frac{y \ln (- 1 + x) + e^{x + 1} x^{3} + 7 e^{x + 1} x y^{2}}{\ln (- 1 + x) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10700	$y^{'} = \frac{- y e^{x} + x y - x^{3} \ln (x) - x^{3} - x y^{2} \ln (x) - x y^{2}}{(- e^{x} + x) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10702	$y^{'} = \frac{y \ln (x) x - y + 2 x^{5} b + 2 x^{3} a y^{2}}{(\ln (x) x - 1) x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10752	$y^{'} = \frac{x y + x^{3} + x y^{2} + y^{3}}{x^{2}}$	[[_homogeneous, ‘class D‘], _rational, _Abel]	✓

10771	$y^{'} = \frac{x y + x + y^{2}}{(- 1 + x) (x + y)}$	[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

10777	$y^{'} = \frac{x^{3} y + x^{3} + x y^{2} + y^{3}}{(- 1 + x) x^{3}}$	[[_homogeneous, ‘class D‘], _rational, _Abel]	✓

10784	$y^{'} = \frac{y \ln (x) + \cosh (x) x a y^{2} + \cosh (x) x^{3} b}{x \ln (x)}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10822	$y^{'} = \frac{y (x^{3} + x^{2} y + y^{2})}{x^{2} (- 1 + x) (x + y)}$	[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓

10899	$y^{'} = \frac{\sin (\frac{y}{x}) (y + 2 x^{2} \sin (\frac{y}{2 x}) \cos (\frac{y}{2 x}))}{2 \sin (\frac{y}{2 x}) x \cos (\frac{y}{2 x})}$	[[_homogeneous, ‘class D‘]]	✓

10900	$y^{'} = \frac{\sin (\frac{y}{x}) (y + 2 x^{3} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}))}{2 \sin (\frac{y}{2 x}) x \cos (\frac{y}{2 x})}$	[[_homogeneous, ‘class D‘]]	✓

10955	$y^{'} = \frac{- y \sin (\frac{y}{x}) + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) x^{3} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x})}{2 \cos (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x}$	[[_homogeneous, ‘class D‘]]	✓

10956	$y^{'} = \frac{- y \sin (\frac{y}{x}) + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) x^{2} \sin (\frac{y}{2 x}) \cos (\frac{y}{2 x})}{2 \cos (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x}$	[[_homogeneous, ‘class D‘]]	✓

10961	$y^{'} = \frac{- y \sin (\frac{y}{x}) + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x + 2 \sin (\frac{y}{x}) x^{3} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) x^{4} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x})}{2 \cos (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x}$	[[_homogeneous, ‘class D‘]]	✓

10964	$y^{'} = \frac{- \sin (\frac{y}{x}) y x - y \sin (\frac{y}{x}) + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) x + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) + 2 \sin (\frac{y}{x}) x^{4} \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x})}{2 \cos (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x (x + 1)}$	[[_homogeneous, ‘class D‘]]	✓

10965	$y^{'} = \frac{y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) x + y \sin (\frac{3 y}{2 x}) \cos (\frac{y}{2 x}) + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x + y \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) - \sin (\frac{y}{x}) y x - y \sin (\frac{y}{x}) + 2 \sin (\frac{y}{x}) \cos (\frac{y}{2 x}) \sin (\frac{y}{2 x}) x}{2 \cos (\frac{y}{x}) \sin (\frac{y}{2 x}) x \cos (\frac{y}{2 x}) (x + 1)}$	[[_homogeneous, ‘class D‘]]	✓

10974	$y^{'} = \frac{y (y^{2} + x y + x^{2} + x)}{x^{2}}$	[[_homogeneous, ‘class D‘], _rational, _Abel]	✓

10983	$y^{'} = - F (x) (- a x^{2} + y^{2}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10984	$y^{'} = - F (x) (- x^{2} - 2 x y + y^{2}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10985	$y^{'} = - F (x) (- a y^{2} - b x^{2}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10987	$y^{'} = - F (x) (x^{2} + 2 x y - y^{2}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

10988	$y^{'} = - F (x) (- 7 x y^{2} - x^{3}) + \frac{y}{x}$	[[_homogeneous, ‘class D‘], _Riccati]	✓

11927	$y^{'} = f (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

11996	$(a x^{2} + b x + e) (- y + x y^{'}) - y^{2} + x^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

12005	$(a x^{n} + b x^{m} + c) (- y + x y^{'}) + s x^{k} (y^{2} - λ x^{2}) = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

12719	$\frac{2 x y + 1}{y} + \frac{(y - x) y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

12720	$\frac{- 2 x^{2} + y^{2}}{x y^{2} - x^{3}} + \frac{(2 y^{2} - x^{2}) y^{'}}{y^{3} - x^{2} y} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

12722	$y + x + x y^{'} = 0$	[_linear]	✓

12728	$e^{\frac{y}{x}} x + y - x y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

12729	$2 x^{2} y + 3 y^{3} - (x^{3} + 2 x y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

12730	$x^{2} y^{'} + y^{2} - x y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

12731	$2 x^{2} y + y^{3} - x^{3} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

12732	$y^{3} + x^{3} y^{'} = 0$	[_separable]	✓

12733	$x + y \cos (\frac{y}{x}) - x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

12751	$y^{2} (3 y - 6 x y^{'}) - x (y - 2 x y^{'}) = 0$	[_separable]	✓

12753	$x^{2} y^{'} + y^{2} - x y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

12755	$x + y - y^{'} (x - y) = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

12756	$x^{2} + y^{2} - 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

12758	$- y + x y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

12759	$3 x^{2} + 6 x y + 3 y^{2} + (2 x^{2} + 3 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

12762	$x^{3} y - y^{4} + (x y^{3} - x^{4}) y^{'} = 0$	[_separable]	✓

12763	$y^{2} - x^{2} + 2 m x y + (m y^{2} - m x^{2} - 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

12764	$x y^{'} - y + 2 x^{2} y - x^{3} = 0$	[_linear]	✓

12766	$x + y y^{'} + y - x y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

12774	$(y - x) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

12777	$x \sin (\frac{y}{x}) - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

12785	$y + x y^{2} - x y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

12790	$y^{3} - 2 x^{2} y + (2 x y^{2} - x^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

12793	$1 + e^{\frac{y}{x}} + e^{\frac{x}{y}} (1 - \frac{x}{y}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

12946	$x^{'} = \frac{2 x}{t}$	[_separable]	✓

12947	$x^{'} = - \frac{t}{x}$	[_separable]	✓

12952	$2 t x^{'} = x$	[_separable]	✓

12973	$x^{'} = \frac{2 x}{t + 1}$	[_separable]	✓

12991	$x^{'} = \frac{4 t^{2} + 3 x^{2}}{2 t x}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

12994	$y^{'} = \frac{y^{2} + 2 t y}{t^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

13009	$x^{'} = (a + \frac{b}{t}) x$ i.c.	[_separable]	✓

13013	$R^{'} = \frac{R}{t} + t e^{- t}$ i.c.	[_linear]	✓

13015	$x^{'} = 2 t x$	[_separable]	✓

13020	$x^{'} + p (t) x = 0$	[_separable]	✓

13021	$x^{'} = \frac{2 x}{3 t} + \frac{2 t}{x}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

13024	$t^{2} y^{'} + 2 t y - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

13027	$x^{3} + 3 t x^{2} x^{'} = 0$	[_separable]	✓

13031	$x^{2} - t^{2} x^{'} = 0$	[_separable]	✓

13167	$y^{'} + y = x + 1$	[[_linear, ‘class A‘]]	✓

13171	$2 x y y^{'} + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓

13193	$3 x + 2 y + (2 x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

13209	$y^{2} + 2 x y - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

13211	$4 x y + y^{'} (x^{2} + 1) = 0$	[_separable]	✓

13218	$x + y - x y^{'} = 0$	[_linear]	✓

13219	$2 x y + 3 y^{2} - (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

13220	$v^{3} + (u^{3} - u v^{2}) v^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

13221	$x \tan (\frac{y}{x}) + y - x y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

13222	$(2 s^{2} + 2 s t + t^{2}) s^{'} + s^{2} + 2 s t - t^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

13228	$x^{2} + 3 y^{2} - 2 x y y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

13229	$2 x - 5 y + (4 x - y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

13230	$3 x^{2} + 9 x y + 5 y^{2} - (6 x^{2} + 4 x y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

13231	$x + 2 y + (2 x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

13232	$3 x - y - (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

13233	$x^{2} + 2 y^{2} + (4 x y - y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

13234	$2 x^{2} + 2 x y + y^{2} + (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

13249	$y^{'} - \frac{y}{x} = - \frac{y^{2}}{x}$	[_separable]	✓

13272	$6 x^{2} y - (x^{3} + 1) y^{'} = 0$	[_separable]	✓

13276	$3 x - 5 y + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

13277	$e^{2 x} y^{2} + (e^{2 x} y - 2 y) y^{'} = 0$	[_separable]	✓

13279	$2 x^{2} + x y + y^{2} + 2 x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

13282	$y^{'} = \frac{2 x - 7 y}{3 y - 8 x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

13285	$y^{'} = \frac{2 x^{2} + y^{2}}{2 x y - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

13286	$x^{2} + y^{2} - 2 x y y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

13291	$y^{'} = \frac{2 x + 7 y}{2 x - 2 y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

13292	$y^{'} = \frac{x y}{x^{2} + 1}$ i.c.	[_separable]	✓

13642	$x^{'} = t^{2} x$	[_separable]	✓

13646	$x y^{'} = k y$	[_separable]	✓

13647	$i^{'} = p (t) i$	[_separable]	✓

13648	$x^{'} = λ x$	[_quadrature]	✓

13668	$x y + y^{2} + x^{2} - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

13781	$x^{'} = e^{\frac{x}{t}} + \frac{x}{t}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

13783	$y = x y^{'} + \frac{1}{y}$	[_separable]	✓

13798	$(x - y) y - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

13800	$x^{'} = \frac{x}{t} + \frac{x^{2}}{t^{3}}$ i.c.	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

13810	$(x - y) y - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

13816	$(y^{2} - x^{2}) y^{'} + 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

13889	$5 y^{'} - x y = 0$	[_separable]	✓

14083	$y - x y^{'} = 0$	[_separable]	✓

14088	$z - (- a^{2} + t^{2}) z^{'} = 0$	[_separable]	✓

14091	$r^{'} + r \tan (t) = 0$	[_separable]	✓

14096	$y - x + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14097	$y + x + x y^{'} = 0$	[_linear]	✓

14098	$x + y + (y - x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14100	$(7 x + 5 y) y^{'} + 10 x + 8 y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14102	$t - s + t s^{'} = 0$	[_linear]	✓

14103	$x y^{2} y^{'} = x^{3} + y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

14104	$x \cos (\frac{y}{x}) (x y^{'} + y) = y \sin (\frac{y}{x}) (- y + x y^{'})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

14132	$\frac{x}{{(x + y)}^{2}} + \frac{(2 x + y) y^{'}}{{(x + y)}^{2}} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

14133	$\frac{1}{x^{2}} + \frac{3 y^{2}}{x^{4}} = \frac{2 y y^{'}}{x^{3}}$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓

14134	$\frac{x^{2} y^{'}}{{(x - y)}^{2}} - \frac{y^{2}}{{(x - y)}^{2}} = 0$	[_separable]	✓

14142	$y = x y^{'} + y^{'}$	[_separable]	✓

14145	$y^{'} = \frac{2 y}{x} - \sqrt{3}$	[_linear]	✓

14197	$\frac{x^{2} y^{'}}{{(x - y)}^{2}} - \frac{y^{2}}{{(x - y)}^{2}} = 0$	[_separable]	✓

14200	$y^{'} (x^{2} + 1) - x y - α = 0$	[_linear]	✓

14201	$x \cos (\frac{y}{x}) y^{'} = y \cos (\frac{y}{x}) - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

14232	$- y + x y^{'} = 0$	[_separable]	✓

14237	$y^{'} - \frac{y}{x} = 1$	[_linear]	✓

14239	$2 x y + x^{2} y^{'} = 0$	[_separable]	✓

14243	$y^{'} + 3 y = 0$	[_quadrature]	✓

14247	$2 x y^{'} - y = 0$	[_separable]	✓

14254	$y^{'} - 2 x y = 0$	[_separable]	✓

14260	$y^{'} x \ln (x) - (1 + \ln (x)) y = 0$	[_separable]	✓

14278	$y^{'} = x y$	[_separable]	✓

14279	$y^{'} = - x y$	[_separable]	✓

14283	$y^{'} = x y$	[_separable]	✓

14284	$y^{'} = \frac{x}{y}$	[_separable]	✓

14285	$y^{'} = \frac{y}{x}$	[_separable]	✓

14292	$y^{'} = \frac{2 x - y}{x + 3 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14295	$y^{'} = \frac{x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

14299	$y^{'} = \frac{y}{y - x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14311	$y^{'} = \cos (x) + \frac{y}{x}$ i.c.	[_linear]	✓

14328	$y^{'} = 3 y$ i.c.	[_quadrature]	✓

14332	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

14333	$y^{'} = \frac{2 x}{y}$ i.c.	[_separable]	✓

14337	$y - x^{2} y^{'} = 0$ i.c.	[_separable]	✓

14341	$y^{'} = - \frac{y (2 x + y)}{x (x + 2 y)}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

14345	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

14347	$y^{'} = \frac{y}{x} + \sin (x^{2})$ i.c.	[_linear]	✓

14350	$x - y y^{'} = 0$	[_separable]	✓

14351	$y - x y^{'} = 0$	[_separable]	✓

14352	$x^{2} - y + x y^{'} = 0$	[_linear]	✓

14355	$y (2 x - 1) + x (x + 1) y^{'} = 0$	[_separable]	✓

14358	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

14359	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

14385	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14386	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14387	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14388	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

14390	$y^{'} = \frac{x y}{x^{2} + y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

14430	$y^{'} - i y = 0$ i.c.	[_quadrature]	✓

14522	$y^{'} = \frac{y + 1}{t + 1}$	[_separable]	✓

14524	$y^{'} = t^{4} y$	[_separable]	✓

14530	$y^{'} = \frac{t}{y}$	[_separable]	✓

14541	$w^{'} = \frac{w}{t}$	[_separable]	✓

14543	$x^{'} = - t x$ i.c.	[_separable]	✓

14544	$y^{'} = t y$ i.c.	[_separable]	✓

14566	$y^{'} = (t + 1) y$ i.c.	[_separable]	✓

14581	$θ^{'} = 2$	[_quadrature]	✓

14583	$v^{'} = - \frac{v}{R C}$	[_quadrature]	✓

14663	$y^{'} = - \frac{y}{t} + 2$	[_linear]	✓

14671	$y^{'} = - \frac{y}{t} + 2$ i.c.	[_linear]	✓

14686	$y^{'} = 3 y$	[_quadrature]	✓

14694	$y^{'} = t y$	[_separable]	✓

14696	$y^{'} = \frac{t y}{t^{2} + 1}$	[_separable]	✓

14702	$x^{'} = - t x$ i.c.	[_separable]	✓

14904	$y y^{'} = 2 x$	[_separable]	✓

14951	$(- 2 + x) y^{'} = 3 + y$	[_separable]	✓

14966	$y^{'} = \frac{x}{y}$	[_separable]	✓

14968	$x y y^{'} = y^{2} + 9$	[_separable]	✓

14972	$y^{'} = \frac{x}{y}$ i.c.	[_separable]	✓

14986	$y^{'} = \frac{y}{x}$	[_separable]	✓

15002	$y^{'} = \frac{y^{2} - 1}{x y}$ i.c.	[_separable]	✓

15011	$y^{'} = y \sin (x)$	[_separable]	✓

15028	$x y^{'} = y + x^{2} \cos (x)$ i.c.	[_linear]	✓

15032	$- y + x y^{'} = x^{2} e^{- x^{2}}$ i.c.	[_linear]	✓

15037	$x^{2} y^{'} - x y = y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

15038	$y^{'} = \frac{x}{y} + \frac{y}{x}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

15039	$\cos (\frac{y}{x}) (y^{'} - \frac{y}{x}) = 1 + \sin (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

15040	$y^{'} = \frac{x - y}{x + y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

15042	$y^{'} - \frac{3 y}{x} = \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

15044	$y^{'} - \frac{y}{x} = \frac{1}{y}$ i.c.	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

15045	$y^{'} = \frac{y}{x} + \frac{x^{2}}{y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

15050	$(x + y) y^{'} = y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

15051	$(2 x y + 2 x^{2}) y^{'} = x^{2} + 2 x y + 2 y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

15063	$2 x y + y^{2} + (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

15067	$4 x^{3} y + (x^{4} - y^{4}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

15089	$x^{3} + y^{3} + x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

15092	$3 x y^{3} - y + x y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

15101	$x y y^{'} = 2 x^{2} + 2 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

15103	$y^{'} = \frac{x + 2 y}{2 x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

15104	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

15110	$x y y^{'} = y^{2} + x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

15112	$x y^{3} y^{'} = y^{4} - x^{2}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

15710	$2 x - y - y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

15711	$y^{'} + 2 y = 0$	[_quadrature]	✓

15712	$y^{'} + x y = 0$	[_separable]	✓

15723	$y^{'} = - \frac{x}{y}$	[_separable]	✓

15725	$y^{'} = - \frac{2 y}{x} - 3$	[_linear]	✓

15741	$y^{'} + 2 y = 0$ i.c.	[_quadrature]	✓

15754	$y^{'} = \frac{2 x y + y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

15763	$y^{'} + \cos (x) y = 0$	[_separable]	✓

15771	$2 x - 3 y + (2 y - 3 x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

15788	$y^{'} = y \sqrt{t}$ i.c.	[_separable]	✓

15790	$t y^{'} = y$	[_separable]	✓

15791	$y^{'} = y \tan (t)$ i.c.	[_separable]	✓

15813	$y^{'} = - \frac{t}{y}$ i.c.	[_separable]	✓

15822	$y^{'} = \frac{y + 1}{t + 1}$	[_separable]	✓

15827	$y^{'} + k y = 0$	[_quadrature]	✓

15860	$y^{'} = \sqrt{\frac{y}{t}}$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

15871	$y^{'} = y \cos (t)$ i.c.	[_separable]	✓

15874	$y^{'} + y f (t) = 0$ i.c.	[_separable]	✓

15880	$y^{'} = 3 y$	[_quadrature]	✓

15881	$y^{'} = - y$	[_quadrature]	✓

15885	$y^{'} = y f (t)$ i.c.	[_separable]	✓

15892	$t y^{'} + y = t$	[_linear]	✓

15908	$x^{'} = \frac{3 x t^{2}}{- t^{3} + 1}$	[_separable]	✓

15909	$p^{'} = t^{3} + \frac{p}{t}$	[_linear]	✓

15921	$y^{'} - \frac{y}{t} = \ln (t)$	[_linear]	✓

15946	$\frac{t}{\sqrt{t^{2} + y^{2}}} + \frac{y y^{'}}{\sqrt{t^{2} + y^{2}}} = 0$	[_separable]	✓

15947	$y \cos (t y) + t \cos (t y) y^{'} = 0$	[_separable]	✓

15949	$3 t y^{2} + y^{3} y^{'} = 0$	[_separable]	✓

15953	$e^{t y} + \frac{t e^{t y} y^{'}}{y} = 0$	[_separable]	✓

15956	$y^{2} + 2 t y y^{'} = 0$	[_separable]	✓

15957	$\frac{3 t^{2}}{y} - \frac{t^{3} y^{'}}{y^{2}} = 0$	[_separable]	✓

15960	$2 t y + (t^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

15963	$3 t^{2} + 3 y^{2} + 6 t y y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓

15966	$- 2 t y^{2} \sin (t^{2}) + 2 y \cos (t^{2}) y^{'} = 0$	[_separable]	✓

15972	$- \frac{y^{2} e^{\frac{y}{t}}}{t^{2}} + 1 + e^{\frac{y}{t}} (1 + \frac{y}{t}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓

15973	$2 t \sin (\frac{y}{t}) - y \cos (\frac{y}{t}) + t \cos (\frac{y}{t}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓

15974	$2 t y^{2} + 2 t^{2} y y^{'} = 0$ i.c.	[_separable]	✓

15975	$1 + \frac{y}{t^{2}} - \frac{y^{'}}{t} = 0$ i.c.	[_linear]	✓

15986	$t^{2} y + t^{3} y^{'} = 0$	[_separable]	✓

15987	$y (2 e^{t} + 4 t) + 3 (e^{t} + t^{2}) y^{'} = 0$	[_separable]	✓

15989	$2 t y + y^{2} - t^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

15992	$5 t y^{2} + y + (2 t^{3} - t) y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

15996	$2 t + 2 y + (2 t + 2 y) y^{'} = 0$	[_quadrature]	✓

15997	$\frac{9 t}{5} + 2 y + (2 t + 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

15998	$2 t + \frac{19 y}{10} + (\frac{19 t}{10} + 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

16002	$t y^{'} - y = t y^{3} \sin (t)$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓

16005	$y^{'} - \frac{y}{t} = t y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

16006	$y^{'} - \frac{y}{t} = \frac{y^{2}}{t^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

16007	$y^{'} - \frac{y}{t} = \frac{y^{2}}{t}$	[_separable]	✓

16009	$\cos (\frac{t}{y + t}) + e^{\frac{2 y}{t}} y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

16010	$y \ln (\frac{t}{y}) + \frac{t^{2} y^{'}}{y + t} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

16012	$\frac{2}{t} + \frac{1}{y} + \frac{t y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

16015	$2 t + (y - 3 t) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

16016	$2 y - 3 t + t y^{'} = 0$	[_linear]	✓

16017	$t y - y^{2} + t (t - 3 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

16018	$t^{2} + t y + y^{2} - t y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

16019	$t^{3} + y^{3} - t y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

16020	$y^{'} = \frac{t + 4 y}{4 t + y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

16021	$t - y + t y^{'} = 0$	[_linear]	✓

16022	$y + (y + t) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

16023	$2 t^{2} - 7 t y + 5 y^{2} + t y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

16025	$y^{2} = (t y - 4 t^{2}) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

16027	$(t^{2} - y^{2}) y^{'} + y^{2} + t y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

16028	$t y y^{'} - t^{2} e^{- \frac{y}{t}} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

16029	$y^{'} = \frac{1}{\frac{2 y e^{- \frac{t}{y}}}{t} + \frac{t}{y}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

16034	$t + y - t y^{'} = 0$ i.c.	[_linear]	✓

16037	$y^{3} - t^{3} - t y^{2} y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

16038	$t y^{3} - (t^{4} + y^{4}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

16039	$y^{4} + (t^{4} - t y^{3}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

16044	$y^{'} - \frac{2 y}{x} = - x^{2} y$	[_separable]	✓

16056	$y^{'} = \frac{y^{2} - t^{2}}{t y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

16057	$y \sin (\frac{t}{y}) - (t + t \sin (\frac{t}{y})) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _dAlembert]	✓

16060	$y^{'} - \frac{y}{t} = \frac{y^{2}}{t}$	[_separable]	✓

16067	$3 t + (t - 4 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓

16068	$y - t + (y + t) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

16070	$y^{2} + (t^{2} + t y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

16071	$r^{'} = \frac{r^{2} + t^{2}}{r t}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

16072	$x^{'} = \frac{5 t x}{x^{2} + t^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

16084	$y - t y^{'} = 2 y^{2} \ln (t)$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓

16097	$y^{'} = - \frac{y}{t - 2}$ i.c.	[_separable]	✓

16586	$y^{'} = \frac{x}{y}$	[_separable]	✓

16609	$y^{'} = \frac{y + 1}{- 1 + x}$	[_separable]	✓

16610	$y^{'} = \frac{x + y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

16614	$y^{'} = - \frac{y}{x}$	[_separable]	✓

16615	$y^{'} = 1$	[_quadrature]	✓

16617	$y^{'} = y$	[_quadrature]	✓

16623	$x y^{'} = 2 x - y$ i.c.	[_linear]	✓

16626	$y^{'} \sin (x) - \cos (x) y = 0$ i.c.	[_separable]	✓

16642	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

16643	$\cos (y^{'}) = 0$	[_quadrature]	✓

16644	$e^{y^{'}} = 1$	[_quadrature]	✓

16647	$\tan (y^{'}) = 0$	[_quadrature]	✓

16655	$(x + 1) y^{'} = y - 1$	[_separable]	✓

16658	$x y^{'} = y + x \cos {(\frac{y}{x})}^{2}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

16659	$x - y + x y^{'} = 0$	[_linear]	✓

16661	$x^{2} y^{'} = x^{2} - x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

16663	$2 x^{2} y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

16664	$4 x - 3 y + (2 y - 3 x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

16665	$y - x + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

16698	$x y^{'} + y = 2 x$	[_linear]	✓

16702	$3 x y^{2} y^{'} - 2 y^{3} = x^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

16704	$y^{'} + 3 x y = y e^{x^{2}}$	[_separable]	✓

16715	$x (2 x^{2} + y^{2}) + y (x^{2} + 2 y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

16719	$2 x + \frac{x^{2} + y^{2}}{x^{2} y} = \frac{(x^{2} + y^{2}) y^{'}}{x y^{2}}$	[[_homogeneous, ‘class D‘], _exact, _rational]	✓

16722	$\frac{x y}{\sqrt{x^{2} + 1}} + 2 x y - \frac{y}{x} + (\sqrt{x^{2} + 1} + x^{2} - \ln (x)) y^{'} = 0$	[_separable]	✓

16725	$\frac{2 x}{y^{3}} + \frac{(y^{2} - 3 x^{2}) y^{'}}{y^{4}} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

16727	$3 x^{2} y + y^{3} + (x^{3} + 3 x y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

16729	$x^{2} + y - x y^{'} = 0$	[_linear]	✓

16791	$x^{3} - 3 x y^{2} + (y^{3} - 3 x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

16792	$5 x y - 4 y^{2} - 6 x^{2} + (y^{2} - 8 x y + \frac{5 x^{2}}{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

16798	$x y y^{'} - y^{2} = x^{4}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

16799	$\frac{1}{x^{2} - x y + y^{2}} = \frac{y^{'}}{2 y^{2} - x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

16803	$y^{'} (3 x^{2} - 2 x) - y (6 x - 2) = 0$	[_separable]	✓

16804	$x y^{2} y^{'} - y^{3} = \frac{x^{4}}{3}$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

16805	$1 + e^{\frac{x}{y}} + e^{\frac{x}{y}} (1 - \frac{x}{y}) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓

16806	$x^{2} + y^{2} - x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

16808	$x y^{2} + y - x y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

16809	$x^{2} + y^{2} + 2 x + 2 y y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

17244	$x^{2} y^{'} = y - x y$ i.c.	[_separable]	✓

17267	$t y^{'} - y = t^{3} e^{- t}$	[_linear]	✓

17294	$t (- 4 + t) y^{'} + y = 0$ i.c.	[_separable]	✓

17299	$y^{'} = \frac{- y + t}{2 t + 5 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

17307	$y^{'} = - \frac{4 t}{y}$ i.c.	[_separable]	✓

17317	$2 x + 4 y + (2 x - 2 y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

17319	$2 x y^{2} + 2 y + (2 x^{2} y + 2 x) y^{'} = 0$	[_separable]	✓

17320	$y^{'} = - \frac{4 x + 2 y}{2 x + 3 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

17321	$y^{'} = - \frac{4 x - 2 y}{2 x - 3 y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

17327	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓

17328	$2 x - y + (- x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

17334	$3 x^{2} y + 2 x y + y^{3} + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational]	✓

17336	$\frac{y^{'}}{\frac{x}{y} - \sin (y)} = 0$	[_quadrature]	✓

17341	$3 x y + y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

17344	$\frac{(3 x^{3} - x y^{2}) y^{'}}{3 x^{2} y + y^{3}} = 1$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

17347	$x y y^{'} = {(x + y)}^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

17348	$y^{'} = \frac{4 y - 7 x}{5 x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

17350	$y^{'} = \frac{y^{4} + 2 x y^{3} - 3 y^{2} x^{2} - 2 x^{3} y}{2 y^{2} x^{2} - 2 x^{3} y - 2 x^{4}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

17351	$(y + x e^{\frac{x}{y}}) y^{'} = y e^{\frac{x}{y}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

17352	$x y y^{'} = x^{2} + y^{2}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

17364	$(3 x - y) x^{'} + 9 y - 2 x = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

17369	$\frac{\sqrt{x} y^{'}}{y} = 1$	[_separable]	✓

17370	$5 x y^{2} + 5 y + (5 x^{2} y + 5 x) y^{'} = 0$	[_separable]	✓

17374	$x^{'} = \frac{2 x y + x^{2}}{3 y^{2} + 2 x y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

17375	$4 x y y^{'} = 8 x^{2} + 5 y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

17812	$y^{'} = 2$	[_quadrature]	✓

17818	$y^{'} = \frac{2 x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

17820	$y^{2} + x^{2} y^{'} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

17821	$(x + y) y^{'} = y - x$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

17822	$x - y \cos (\frac{y}{x}) + x \cos (\frac{y}{x}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

17847	$\frac{2 x}{y^{3}} + \frac{(y^{2} - 3 x^{2}) y^{'}}{y^{4}} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

17978	$x y^{'} = 2 y$	[_separable]	✓

17980	$y^{'} = k y$	[_quadrature]	✓

17984	$x y^{'} = y + x^{2} + y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

17985	$y^{'} = \frac{x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

17986	$2 x y y^{'} = x^{2} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

17988	$y^{'} = \frac{y^{2}}{x y - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18000	$x^{5} y^{'} + y^{5} = 0$	[_separable]	✓

18002	$y^{'} = 2 x y$	[_separable]	✓

18005	$y^{'} + y \tan (x) = 0$	[_separable]	✓

18006	$y^{'} - y \tan (x) = 0$	[_separable]	✓

18025	$x^{2} - 2 y^{2} + x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18026	$x^{2} y^{'} - 3 x y - 2 y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18027	$x^{2} y^{'} = 3 (x^{2} + y^{2}) \arctan (\frac{y}{x}) + x y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

18028	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) + x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

18029	$x y^{'} = y + 2 x e^{- \frac{y}{x}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

18030	$x - y - (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18031	$x y^{'} = 2 x + 3 y$	[_linear]	✓

18033	$x^{2} y^{'} = 2 x y + y^{2}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18034	$x^{3} + y^{3} - x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18048	$y + y \cos (x y) + (x + x \cos (x y)) y^{'} = 0$	[_separable]	✓

18051	$- \frac{\sin (\frac{x}{y})}{y} + \frac{x \sin (\frac{x}{y}) y^{'}}{y^{2}} = 0$	[_separable]	✓

18052	$1 + y + (1 - x) y^{'} = 0$	[_separable]	✓

18061	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓

18064	$\frac{4 y^{2} - 2 x^{2}}{4 x y^{2} - x^{3}} + \frac{(8 y^{2} - x^{2}) y^{'}}{4 y^{3} - x^{2} y} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

18065	$(3 x^{2} - y^{2}) y^{'} - 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

18078	$x y^{'} = x^{5} + x^{3} y^{2} + y$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

18079	$(x + y) y^{'} = y - x$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18080	$x y^{'} = y + x^{2} + 9 y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓

18081	$y^{2} - y + x y^{'} = 0$	[_separable]	✓

18082	$- y + x y^{'} = 2 x^{2} - 3$	[_linear]	✓

18087	$2 x y^{2} - y + x y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

18128	$x y y^{'} = y^{2} + x^{2} y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18131	$x^{2} + y = x y^{'}$	[_linear]	✓

18139	$y^{2} - 3 x y - 2 x^{2} = (x^{2} - x y) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18145	$x^{2} y^{4} + x^{6} - x^{3} y^{3} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18147	$y^{'} = 1 + \frac{y}{x} - \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

18148	$y^{'} = \frac{2 x y e^{\frac{x^{2}}{y^{2}}}}{y^{2} + y^{2} e^{\frac{x^{2}}{y^{2}}} + 2 x^{2} e^{\frac{x^{2}}{y^{2}}}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

18152	$\frac{y - x}{{(x + y)}^{3}} - \frac{2 x y^{'}}{{(x + y)}^{3}} = 0$	[_linear]	✓

18155	$3 x^{2} y - y^{3} - (3 x y^{2} - x^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

18161	$3 x y + y^{2} + (3 x y + x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18162	$x^{2} y^{'} = y^{2} + x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

18167	$x^{2} y^{'} - y^{2} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18423	$x^{'} = \cos (\frac{x}{t})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

18424	$(t^{2} - x^{2}) x^{'} = t x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

18428	$x^{'} + x \tan (t) = 0$	[_separable]	✓

18435	$x^{'} = - λ x$	[_quadrature]	✓

18460	$v^{'} + \frac{2 v}{u} = 3$	[_linear]	✓

18466	$y^{2} = x (y - x) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18467	$2 x^{2} y + y^{3} - x^{3} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18470	$x + y y^{'} = m y$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18471	$\frac{2 x}{y^{3}} + (\frac{1}{y^{2}} - \frac{3 x^{2}}{y^{4}}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

18476	$p^{'} = \frac{p + a t^{3} - 2 p t^{2}}{t (- t^{2} + 1)}$	[_linear]	✓

18492	$v^{'} + \frac{2 v}{u} = 3 v$	[_separable]	✓

18495	$\frac{y^{'}}{x} = y \sin (x^{2} - 1) - \frac{2 y}{\sqrt{x}}$	[_separable]	✓

18496	$y^{'} = 1 + \frac{2 y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18545	$x (- x^{2} + 1) y^{'} + (x^{2} - 1) y = x^{3}$	[_linear]	✓

18547	$x (- x^{2} + 1) y^{'} + (2 x^{2} - 1) y = a x^{3}$	[_linear]	✓

18561	$x (x - 2 y) y^{'} + x^{2} + 2 y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18562	$5 x y y^{'} - x^{2} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18563	$(x^{2} + 3 x y - y^{2}) y^{'} - 3 y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

18564	$(x^{2} + 2 x y) y^{'} - 3 x^{2} + 2 x y - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18565	$5 x y y^{'} - 4 x^{2} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18566	$(x^{2} - 2 x y) y^{'} + x^{2} - 3 x y + 2 y^{2} = 0$	[_linear]	✓

18567	$3 x^{2} y^{'} + 2 x^{2} - 3 y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓

18652	$x^{2} + y^{2} - 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18653	$y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18654	$x^{2} y - (x^{3} + y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

18655	$(4 y + 3 x) y^{'} + y - 2 x = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18658	$x^{2} - 4 x y - 2 y^{2} + (y^{2} - 4 x y - 2 x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

18663	$y - x y^{'} + \ln (x) = 0$	[_linear]	✓

18666	$x^{4} e^{x} - 2 m x y^{2} + 2 m x^{2} y y^{'} = 0$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓

18668	$x^{2} y - 2 x y^{2} - (x^{3} - 3 x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18670	$x^{2} + y^{2} + 2 x + 2 y y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

18674	$y^{3} - 2 x^{2} y + (2 x y^{2} - x^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

18696	$x y^{'} + \frac{y^{2}}{x} = y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

18699	$x^{2} y - (x^{3} + y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

18700	$x (- x^{2} + 1) y^{'} + (2 x^{2} - 1) y = a x^{3}$	[_linear]	✓

18702	$x + y y^{'} = m (- y + x y^{'})$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18710	$y y^{'} = a x$	[_separable]	✓

18712	$(x + y) y^{'} + x - y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18714	$2 x y + (y^{2} - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

18719	$y^{2} + x^{2} y^{'} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

18742	$x y (y - x y^{'}) = x + y y^{'}$	[_separable]	✓

18968	$y + x + x y^{'} = 0$	[_linear]	✓

18969	$y (1 + x y) - x y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓

18971	$y - x + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18973	$x^{3} + 3 x y^{2} + (3 x^{2} y + y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

18976	$x y^{'} - y - \cos (\frac{1}{x}) = 0$	[_linear]	✓

18977	$x + y y^{'} = m (- y + x y^{'})$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

18981	$2 y + (x^{2} + 1) \arctan (x) y^{'} = 0$	[_separable]	✓

18997	$(x^{2} + y^{2}) y^{'} = x^{2} + x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

18998	$(x \cos (\frac{y}{x}) + y \sin (\frac{y}{x})) y - (y \sin (\frac{y}{x}) - x \cos (\frac{y}{x})) x y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

18999	$x^{2} - y^{2} + 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

19000	$y^{'} = \frac{y}{x} + \tan (\frac{y}{x})$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

19003	$y^{2} = (x y - x^{2}) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

19004	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) - x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

19005	$(x^{2} + y^{2}) y^{'} = x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

19006	$x^{2} y^{'} + (x + y) y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

19007	$2 y^{'} = \frac{y}{x} + \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

19012	$x (x^{2} + 3 y^{2}) + y (3 x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓

19013	$x^{2} + 3 y^{2} - 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

19040	$x^{2} y - 2 x y^{2} - (x^{3} - 3 x^{2} y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

19044	$x^{2} + y^{2} - 2 x y y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

19058	$x + y y^{'} = m (- y + x y^{'})$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

19075	$y^{2} + x^{2} y^{'} = x y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

19179	$y = x y^{'} + x \sqrt{1 + {y^{'}}^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓

19186	$y - x y^{'} = x + y y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓

19201	$(x \cos (\frac{y}{x}) + y \sin (\frac{y}{x})) y = (y \sin (\frac{y}{x}) - x \cos (\frac{y}{x})) x y^{'}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓

19430	$y - x y^{'} = 0$	[_separable]	✓

19435	$1 + y^{2} - x y y^{'} = 0$	[_separable]	✓

19436	$y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓

19445	$x^{2} y - (x^{3} + y^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

19449	$y^{3} - 2 x^{2} y + (2 x y^{2} - x^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓

19481	$x y (y - x y^{'}) = x + y y^{'}$	[_separable]	✓

2.3.7 ﬁrst order ode homogD2