ﬁrst order ode linear

Table 2.395: ﬁrst order ode linear


#	ODE	CAS classiﬁcation	Solved?

19	$y^{'} = - y - \sin (x)$	[[_linear, ‘class A‘]]	✓

20	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓

21	$y^{'} = y - \sin (x)$	[[_linear, ‘class A‘]]	✓

22	$y^{'} = x - y$	[[_linear, ‘class A‘]]	✓

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

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

25	$y^{'} = x^{2} - y$	[[_linear, ‘class A‘]]	✓

26	$y^{'} = x^{2} - y - 2$	[[_linear, ‘class A‘]]	✓

37	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓

38	$y^{'} = y - x$ i.c.	[[_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]	✓

57	$y^{'} = 1 + x + y + x y$	[_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]	✓

74	$y^{'} - 2 y = 3 e^{2 x}$ i.c.	[[_linear, ‘class A‘]]	✓

75	$y^{'} + 3 y = 2 x e^{- 3 x}$	[[_linear, ‘class A‘]]	✓

76	$y^{'} - 2 x y = e^{x^{2}}$	[_linear]	✓

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

78	$x y^{'} + 5 y = 7 x^{2}$ i.c.	[_linear]	✓

79	$2 x y^{'} + y = 10 \sqrt{x}$	[_linear]	✓

80	$3 x y^{'} + y = 12 x$	[_linear]	✓

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

82	$2 x y^{'} - 3 y = 9 x^{3}$	[_linear]	✓

83	$x y^{'} + y = 3 x y$ i.c.	[_separable]	✓

84	$x y^{'} + 3 y = 2 x^{5}$ i.c.	[_linear]	✓

85	$y^{'} + y = e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓

86	$x y^{'} - 3 y = x^{3}$ i.c.	[_linear]	✓

87	$y^{'} + 2 x y = x$ i.c.	[_separable]	✓

88	$y^{'} = (1 - y) \cos (x)$ i.c.	[_separable]	✓

89	$(x + 1) y^{'} + y = \cos (x)$ i.c.	[_linear]	✓

90	$x y^{'} = 2 y + x^{3} \cos (x)$	[_linear]	✓

91	$y^{'} + y \cot (x) = \cos (x)$	[_linear]	✓

92	$y^{'} = 1 + x + y + x y$ i.c.	[_separable]	✓

93	$x y^{'} = 3 y + x^{4} \cos (x)$ i.c.	[_linear]	✓

94	$y^{'} = 2 x y + 3 x^{2} e^{x^{2}}$ i.c.	[_linear]	✓

95	$x y^{'} + (2 x - 3) y = 4 x^{4}$	[_linear]	✓

96	$(x^{2} + 4) y^{'} + 3 x y = x$ i.c.	[_separable]	✓

97	$(x^{2} + 1) y^{'} + 3 x^{3} y = 6 x e^{- \frac{3 x^{2}}{2}}$ i.c.	[_linear]	✓

98	$\frac{1 - 4 x y^{2}}{x^{'}} = y^{3}$	[_linear]	✓

99	$\frac{x + y e^{y}}{x^{'}} = 1$	[[_linear, ‘class A‘]]	✓

100	$\frac{1 + 2 x y}{x^{'}} = y^{2} + 1$	[_linear]	✓

101	$y^{'} = 2 x y + 1$	[_linear]	✓

102	$2 x y^{'} = y + 2 x \cos (x)$ i.c.	[_linear]	✓

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

104	$y^{'} + p (x) y = q (x)$	[_linear]	✓

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]	✓

179	$x^{3} + 3 y - x y^{'} = 0$	[_linear]	✓

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

185	$2 x^{2} y + x^{3} y^{'} = 1$	[_linear]	✓

193	$y^{'} + 3 y = 3 x^{2} e^{- 3 x}$	[[_linear, ‘class A‘]]	✓

198	$x y^{'} + 3 y = \frac{3}{x^{3 / 2}}$	[_linear]	✓

199	$(x^{2} - 1) y^{'} + (- 1 + x) y = 1$	[_linear]	✓

203	$2 y + (x + 1) y^{'} = 3 x + 3$	[_linear]	✓

206	$x y^{'} + y = 2 e^{2 x}$	[_linear]	✓

207	$(2 x + 1) y^{'} + y = {(2 x + 1)}^{3 / 2}$	[_linear]	✓

209	$y^{'} = 3 (y + 7) x^{2}$	[_separable]	✓

213	$y^{'} = \frac{2 x y + 2 x}{x^{2} + 1}$	[_separable]	✓

661	$y^{'} = - y - \sin (x)$	[[_linear, ‘class A‘]]	✓

662	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓

663	$y^{'} = y - \sin (x)$	[[_linear, ‘class A‘]]	✓

664	$y^{'} = x - y$	[[_linear, ‘class A‘]]	✓

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

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

667	$y^{'} = x^{2} - y$	[[_linear, ‘class A‘]]	✓

668	$y^{'} = x^{2} - y - 2$	[[_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]	✓

692	$y^{'} = 1 + x + y + x y$	[_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]	✓

705	$y^{'} - 2 y = 3 e^{2 x}$ i.c.	[[_linear, ‘class A‘]]	✓

706	$y^{'} + 3 y = 2 x e^{- 3 x}$	[[_linear, ‘class A‘]]	✓

707	$y^{'} - 2 x y = e^{x^{2}}$	[_linear]	✓

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

709	$2 x y^{'} + y = 10 \sqrt{x}$ i.c.	[_linear]	✓

710	$2 x y^{'} + y = 10 \sqrt{x}$	[_linear]	✓

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

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

713	$2 x y^{'} - 3 y = 9 x^{3}$	[_linear]	✓

714	$x y^{'} + y = 3 x y$ i.c.	[_separable]	✓

715	$x y^{'} + 3 y = 2 x^{5}$ i.c.	[_linear]	✓

716	$y^{'} + y = e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓

717	$x y^{'} - 3 y = x^{3}$ i.c.	[_linear]	✓

718	$y^{'} + 2 x y = x$ i.c.	[_separable]	✓

719	$y^{'} = (1 - y) \cos (x)$ i.c.	[_separable]	✓

720	$(x + 1) y^{'} + y = \cos (x)$ i.c.	[_linear]	✓

721	$x y^{'} = 2 y + x^{3} \cos (x)$	[_linear]	✓

722	$y^{'} + y \cot (x) = \cos (x)$	[_linear]	✓

723	$y^{'} = 1 + x + y + x y$ i.c.	[_separable]	✓

724	$x y^{'} = 3 y + x^{4} \cos (x)$ i.c.	[_linear]	✓

725	$y^{'} = 2 x y + 3 x^{2} e^{x^{2}}$ i.c.	[_linear]	✓

726	$x y^{'} + (2 x - 3) y = 4 x^{4}$	[_linear]	✓

727	$(x^{2} + 4) y^{'} + 3 x y = x$ i.c.	[_separable]	✓

728	$(x^{2} + 1) y^{'} + 3 x^{3} y = 6 x e^{- \frac{3 x^{2}}{2}}$ i.c.	[_linear]	✓

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]	✓

771	$x^{3} + 3 y - x y^{'} = 0$	[_linear]	✓

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

777	$2 x^{2} y + x^{3} y^{'} = 1$	[_linear]	✓

785	$y^{'} + 3 y = 3 x^{2} e^{- 3 x}$	[[_linear, ‘class A‘]]	✓

790	$x y^{'} + 3 y = \frac{3}{x^{3 / 2}}$	[_linear]	✓

791	$(x^{2} - 1) y^{'} + (- 1 + x) y = 1$	[_linear]	✓

795	$2 y + (x + 1) y^{'} = 3 x + 3$	[_linear]	✓

798	$x y^{'} + y = 2 e^{2 x}$	[_linear]	✓

799	$(2 x + 1) y^{'} + y = {(2 x + 1)}^{3 / 2}$	[_linear]	✓

800	$y^{'} = 3 (y + 7) x^{2}$	[_separable]	✓

801	$y^{'} = 3 (y + 7) x^{2}$	[_separable]	✓

805	$y^{'} = \frac{2 x y + 2 x}{x^{2} + 1}$	[_separable]	✓

1098	$3 y + y^{'} = e^{- 2 t} + t$	[[_linear, ‘class A‘]]	✓

1099	$- 2 y + y^{'} = e^{2 t} t^{2}$	[[_linear, ‘class A‘]]	✓

1100	$y^{'} + y = 1 + t e^{- t}$	[[_linear, ‘class A‘]]	✓

1101	$\frac{y}{t} + y^{'} = 3 \cos (2 t)$	[_linear]	✓

1102	$- 2 y + y^{'} = 3 e^{t}$	[[_linear, ‘class A‘]]	✓

1103	$2 y + t y^{'} = \sin (t)$	[_linear]	✓

1104	$2 t y + y^{'} = 2 t e^{- t^{2}}$	[_linear]	✓

1105	$4 t y + (t^{2} + 1) y^{'} = \frac{1}{{(t^{2} + 1)}^{2}}$	[_linear]	✓

1106	$y + 2 y^{'} = 3 t$	[[_linear, ‘class A‘]]	✓

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

1108	$y^{'} + y = 5 \sin (2 t)$	[[_linear, ‘class A‘]]	✓

1109	$y + 2 y^{'} = 3 t^{2}$	[[_linear, ‘class A‘]]	✓

1110	$- y + y^{'} = 2 e^{2 t} t$ i.c.	[[_linear, ‘class A‘]]	✓

1111	$2 y + y^{'} = t e^{- 2 t}$ i.c.	[[_linear, ‘class A‘]]	✓

1112	$2 y + t y^{'} = t^{2} - t + 1$ i.c.	[_linear]	✓

1113	$\frac{2 y}{t} + y^{'} = \frac{\cos (t)}{t^{2}}$ i.c.	[_linear]	✓

1114	$- 2 y + y^{'} = e^{2 t}$ i.c.	[[_linear, ‘class A‘]]	✓

1115	$2 y + t y^{'} = \sin (t)$ i.c.	[_linear]	✓

1116	$4 t^{2} y + t^{3} y^{'} = e^{- t}$ i.c.	[_linear]	✓

1117	$(t + 1) y + t y^{'} = t$ i.c.	[_linear]	✓

1118	$- \frac{y}{2} + y^{'} = 2 \cos (t)$ i.c.	[[_linear, ‘class A‘]]	✓

1119	$- y + 2 y^{'} = e^{\frac{t}{3}}$ i.c.	[[_linear, ‘class A‘]]	✓

1120	$- 2 y + 3 y^{'} = e^{- \frac{π t}{2}}$ i.c.	[[_linear, ‘class A‘]]	✓

1121	$(t + 1) y + t y^{'} = 2 t e^{- t}$ i.c.	[_linear]	✓

1122	$2 y + t y^{'} = \frac{\sin (t)}{t}$ i.c.	[_linear]	✓

1123	$\cos (t) y + \sin (t) y^{'} = e^{t}$ i.c.	[_linear]	✓

1124	$\frac{y}{2} + y^{'} = 2 \cos (t)$ i.c.	[[_linear, ‘class A‘]]	✓

1125	$\frac{2 y}{3} + y^{'} = 1 - \frac{t}{2}$	[[_linear, ‘class A‘]]	✓

1126	$\frac{y}{4} + y^{'} = 3 + 2 \cos (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓

1127	$- y + y^{'} = 1 + 3 \sin (t)$	[[_linear, ‘class A‘]]	✓

1128	$- \frac{3 y}{2} + y^{'} = 2 e^{t} + 3 t$	[[_linear, ‘class A‘]]	✓

1166	$\ln (t) y + (t - 3) y^{'} = 2 t$	[_linear]	✓

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

1168	$\tan (t) y + y^{'} = \sin (t)$ i.c.	[_linear]	✓

1169	$2 t y + (- t^{2} + 4) y^{'} = 3 t^{2}$ i.c.	[_linear]	✓

1170	$2 t y + (- t^{2} + 4) y^{'} = 3 t^{2}$ i.c.	[_linear]	✓

1171	$y + \ln (t) y^{'} = \cot (t)$	[_linear]	✓

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

1202	$\frac{y}{x} + 6 x + (\ln (x) - 2) y^{'} = 0$	[_linear]	✓

1211	$y^{'} = - 1 + e^{2 x} + y$	[[_linear, ‘class A‘]]	✓

1218	$y^{'} = \frac{x^{3} - 2 y}{x}$	[_linear]	✓

1221	$y^{'} = 3 - 6 x + y - 2 x y$	[_separable]	✓

1223	$x y + x y^{'} = 1 - y$ i.c.	[_linear]	✓

1225	$x y^{'} + 2 y = \frac{\sin (x)}{x}$ i.c.	[_linear]	✓

1229	$y^{'} + y = \frac{1}{e^{x} + 1}$	[_linear]	✓

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

1234	$y^{'} = e^{2 x} + 3 y$	[[_linear, ‘class A‘]]	✓

1235	$2 y + y^{'} = e^{- x^{2} - 2 x}$	[[_linear, ‘class A‘]]	✓

1240	$(t + 1) y + t y^{'} = e^{2 t}$	[_linear]	✓

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

1520	$x y^{'} + y = x^{2}$	[_linear]	✓

1521	$y^{'} + 2 x y = x$	[_separable]	✓

1530	$y^{'} = \cos (x) - y \tan (x)$ i.c.	[_linear]	✓

1531	$y^{'} = \frac{x^{2} - 2 x^{2} y + 2}{x^{3}}$ i.c.	[_linear]	✓

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]	✓

1549	$y^{'} + (\frac{1}{x} - 1) y = - \frac{2}{x}$	[_linear]	✓

1550	$y^{'} + 2 x y = x e^{- x^{2}}$	[_linear]	✓

1551	$y^{'} + \frac{2 x y}{x^{2} + 1} = \frac{e^{- x^{2}}}{x^{2} + 1}$	[_linear]	✓

1552	$y^{'} + \frac{y}{x} = \frac{7}{x^{2}} + 3$	[_linear]	✓

1553	$y^{'} + \frac{4 y}{- 1 + x} = \frac{1}{{(- 1 + x)}^{5}} + \frac{\sin (x)}{{(- 1 + x)}^{4}}$	[_linear]	✓

1554	$x y^{'} + (2 x^{2} + 1) y = x^{3} e^{- x^{2}}$	[_linear]	✓

1555	$x y^{'} + 2 y = \frac{2}{x^{2}} + 1$	[_linear]	✓

1556	$y^{'} + y \tan (x) = \cos (x)$	[_linear]	✓

1557	$2 y + (x + 1) y^{'} = \frac{\sin (x)}{x + 1}$	[_linear]	✓

1558	$(- 2 + x) (- 1 + x) y^{'} - (4 x - 3) y = {(- 2 + x)}^{3}$	[_linear]	✓

1559	$y^{'} + 2 \sin (x) \cos (x) y = e^{- \sin {(x)}^{2}}$	[_linear]	✓

1560	$x^{2} y^{'} + 3 x y = e^{x}$	[_linear]	✓

1561	$y^{'} + 7 y = e^{3 x}$ i.c.	[[_linear, ‘class A‘]]	✓

1562	$(x^{2} + 1) y^{'} + 4 x y = \frac{2}{x^{2} + 1}$ i.c.	[_linear]	✓

1563	$x y^{'} + 3 y = \frac{2}{x (x^{2} + 1)}$ i.c.	[_linear]	✓

1564	$y^{'} + y \cot (x) = \cos (x)$ i.c.	[_linear]	✓

1565	$y^{'} + \frac{y}{x} = \frac{2}{x^{2}} + 1$ i.c.	[_linear]	✓

1566	$(- 1 + x) y^{'} + 3 y = \frac{1}{{(- 1 + x)}^{3}} + \frac{\sin (x)}{{(- 1 + x)}^{2}}$ i.c.	[_linear]	✓

1567	$x y^{'} + 2 y = 8 x^{2}$ i.c.	[_linear]	✓


1568	$x y^{'} - 2 y = - x^{2}$ i.c.	[_linear]	✓

1569	$y^{'} + 2 x y = x$ i.c.	[_separable]	✓

1570	$(- 1 + x) y^{'} + 3 y = \frac{1 + (- 1 + x) \sec {(x)}^{2}}{{(- 1 + x)}^{3}}$ i.c.	[_linear]	✓

1571	$(x + 2) y^{'} + 4 y = \frac{2 x^{2} + 1}{x {(x + 2)}^{3}}$ i.c.	[_linear]	✓

1572	$(x^{2} - 1) y^{'} - 2 x y = x (x^{2} - 1)$ i.c.	[_linear]	✓

1573	$x y^{'} - 2 y = - 1$ i.c.	[_separable]	✓

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

1591	$y^{'} + 2 x (y + 1) = 0$ i.c.	[_separable]	✓

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

1613	$y^{'} = 2 x y$	[_separable]	✓

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

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

1681	$3 y \cos (x) + 4 x e^{x} + 2 x^{3} y + (3 \sin (x) + 3) y^{'} = 0$	[_linear]	✓

1700	$\sin (x) - y \sin (x) - 2 \cos (x) + \cos (x) y^{'} = 0$ i.c.	[_linear]	✓

1701	$(2 x - 1) (y - 1) + (x + 2) (x - 3) y^{'} = 0$ i.c.	[_separable]	✓

1713	$y - x y^{'} = 0$	[_separable]	✓

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

1716	$5 x y + 2 y + 5 + 2 x y^{'} = 0$	[_linear]	✓

1717	$x y + x + 2 y + 1 + (x + 1) y^{'} = 0$	[_linear]	✓

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

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

1730	$a \cos (x) y - y^{2} \sin (x) + (b \cos (x) y - x \sin (x) y) y^{'} = 0$	[_linear]	✓

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

2294	$y^{'} + \sin (t) y = 0$ i.c.	[_separable]	✓

2295	$y^{'} + e^{t^{2}} y = 0$ i.c.	[_separable]	✓

2296	$y^{'} - 2 t y = t$	[_separable]	✓

2297	$2 t y + y^{'} = t$ i.c.	[_separable]	✓

2298	$y^{'} + y = \frac{1}{t^{2} + 1}$ i.c.	[_linear]	✓

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

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

2301	$\frac{2 t y}{t^{2} + 1} + y^{'} = \frac{1}{t^{2} + 1}$	[_linear]	✓

2302	$y^{'} + y = t e^{t}$	[[_linear, ‘class A‘]]	✓

2303	$t^{2} y + y^{'} = 1$	[_linear]	✓

2304	$t^{2} y + y^{'} = t^{2}$	[_separable]	✓

2305	$\frac{t y}{t^{2} + 1} + y^{'} = 1 - \frac{t^{3} y}{t^{4} + 1}$	[_linear]	✓

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

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

2308	$y^{'} - 2 t y = t$ i.c.	[_separable]	✓

2309	$t y + y^{'} = t + 1$ i.c.	[_linear]	✓

2310	$y^{'} + y = \frac{1}{t^{2} + 1}$ i.c.	[_linear]	✓

2311	$y^{'} - 2 t y = 1$ i.c.	[_linear]	✓

2312	$t y + (t^{2} + 1) y^{'} = {(t^{2} + 1)}^{5 / 2}$	[_linear]	✓

2313	$4 t y + (t^{2} + 1) y^{'} = t$ i.c.	[_separable]	✓

2314	$\frac{y}{t} + y^{'} = \frac{1}{t^{2}}$	[_linear]	✓

2315	$y^{'} + \frac{y}{\sqrt{t}} = e^{\frac{\sqrt{t}}{2}}$	[_linear]	✓

2316	$\frac{y}{t} + y^{'} = \cos (t) + \frac{\sin (t)}{t}$	[_linear]	✓

2317	$\tan (t) y + y^{'} = \cos (t) \sin (t)$	[_linear]	✓

2319	$y^{'} = (t + 1) (y + 1)$	[_separable]	✓

2329	$3 t y^{'} = \cos (t) y$ i.c.	[_separable]	✓

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

2360	$y^{'} = t (y + 1)$ i.c.	[_separable]	✓

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

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

2474	$\frac{2 t y}{t^{2} + 1} + y^{'} = \frac{1}{t^{2} + 1}$	[_linear]	✓

2475	$y^{'} + y = t e^{t}$	[[_linear, ‘class A‘]]	✓

2476	$t^{2} y + y^{'} = 1$	[_linear]	✓

2477	$t^{2} y + y^{'} = t^{2}$	[_separable]	✓

2478	$\frac{t y}{t^{2} + 1} + y^{'} = 1 - \frac{t^{3} y}{t^{4} + 1}$	[_linear]	✓

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]	✓

2482	$y^{'} - 2 t y = t$ i.c.	[_separable]	✓

2483	$t y + y^{'} = t + 1$ i.c.	[_linear]	✓

2484	$y^{'} + y = \frac{1}{t^{2} + 1}$ i.c.	[_linear]	✓

2485	$y^{'} - 2 t y = 1$ i.c.	[_linear]	✓

2486	$t y + (t^{2} + 1) y^{'} = {(t^{2} + 1)}^{5 / 2}$	[_linear]	✓

2487	$4 t y + (t^{2} + 1) y^{'} = t$ i.c.	[_separable]	✓

2488	$y^{'} + y = {\begin{array}{cc} 2 & 0 \leq t \leq 1 \\ 0 & 1 < t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

2490	$y^{'} = (t + 1) (y + 1)$	[_separable]	✓

2500	$3 t y^{'} = \cos (t) y$ i.c.	[_separable]	✓

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

2519	$y^{'} = 2 t (y + 1)$ i.c.	[_separable]	✓

2535	$y^{'} = t (y + 1)$ i.c.	[_separable]	✓

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

2844	$x y^{'} + y = 0$	[_separable]	✓

2845	$y^{'} = 2 x y$	[_separable]	✓

2848	$(x + 1) y^{'} - 1 + y = 0$	[_separable]	✓

2849	$\tan (x) y^{'} - y = 1$	[_separable]	✓

2850	$y + 3 + \cot (x) y^{'} = 0$	[_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]	✓

2871	$x + y = x y^{'}$	[_linear]	✓

2922	$y e^{x} - 2 x + e^{x} y^{'} = 0$	[[_linear, ‘class A‘]]	✓

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

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

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

2958	$x y^{'} + 2 y = x^{2}$	[_linear]	✓

2959	$y^{'} - x y = e^{\frac{x^{2}}{2}} \cos (x)$	[_linear]	✓

2960	$y^{'} + 2 x y = 2 x e^{- x^{2}}$	[_linear]	✓

2961	$y^{'} = y + 3 x^{2} e^{x}$	[[_linear, ‘class A‘]]	✓

2962	$x^{'} + x = e^{- y}$	[[_linear, ‘class A‘]]	✓

2963	$x^{'} y + (1 + y) x = e^{y}$	[_linear]	✓

2965	$x y^{'} - 2 x^{4} - 2 y = 0$	[_linear]	✓

2967	$y^{2} x^{'} + (y^{2} + 2 y) x = 1$	[_linear]	✓

2968	$x y^{'} = 5 y + x + 1$	[_linear]	✓

2969	$x^{2} y^{'} + y - 2 x y - 2 x^{2} = 0$	[_linear]	✓

2970	$2 y + (x + 1) y^{'} = \frac{e^{x}}{x + 1}$	[_linear]	✓

2973	$\cos (θ) r^{'} = 2 + 2 r \sin (θ)$	[_linear]	✓

2974	$\sin (θ) r^{'} + 1 + r \tan (θ) = \cos (θ)$	[_linear]	✓

2975	$x^{'} y = 2 y e^{3 y} + x (3 y + 2)$	[_linear]	✓

2977	$y^{'} + y \cot (x) - \sec (x) = 0$	[_linear]	✓

2979	$2 y - x y - 3 + x y^{'} = 0$ i.c.	[_linear]	✓

2981	$(x^{2} - 1) y^{'} + {(x^{2} - 1)}^{2} + 4 y = 0$ i.c.	[_linear]	✓

3004	$(1 - x) y^{'} - y - 1 = 0$	[_separable]	✓

3007	$x \ln (x) y^{'} + y - x = 0$	[_linear]	✓

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

3027	$y^{'} + x + y \cot (x) = 0$	[_linear]	✓

3046	$x y^{'} = x^{4} + 4 y$ i.c.	[_linear]	✓

3051	$2 y + y^{'} = 3 e^{2 x}$ i.c.	[[_linear, ‘class A‘]]	✓

3055	$2 x y - 2 y + 1 + x (- 1 + x) y^{'} = 0$ i.c.	[_linear]	✓

3169	$y^{'} + P (x) y = Q (x)$	[_linear]	✓

3293	${y^{'}}^{3} + (x + y - 2 x y) {y^{'}}^{2} - 2 y^{'} x y (x + y) = 0$	[_quadrature]	✓

3334	$y^{2} - 2 x y y^{'} + {y^{'}}^{2} (x^{2} - 1) = 0$	[_separable]	✓

3409	$y^{'} = x y$	[_separable]	✓

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

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

3440	$y^{'} = 2 y + e^{- 3 t}$	[[_linear, ‘class A‘]]	✓

3441	$y^{'} = 2 y + e^{2 t}$	[[_linear, ‘class A‘]]	✓

3442	$y^{'} = - y + t$	[[_linear, ‘class A‘]]	✓

3443	$2 y + t y^{'} = \sin (t)$	[_linear]	✓

3444	$y^{'} = \tan (t) y + \sec (t)$	[_linear]	✓

3445	$y^{'} = \frac{2 t y}{t^{2} + 1} + t + 1$	[_linear]	✓

3446	$y^{'} = \tan (t) y + \sec {(t)}^{3}$	[_linear]	✓

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

3450	$y^{'} = - \tan (t) y + \sec (t)$ i.c.	[_linear]	✓

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

3452	$t y^{'} = - y + t^{3}$ i.c.	[_linear]	✓

3453	$y^{'} + 4 \tan (2 t) y = \tan (2 t)$ i.c.	[_separable]	✓

3454	$t \ln (t) y^{'} = t \ln (t) - y$ i.c.	[_linear]	✓

3455	$y^{'} = \frac{2 y}{- t^{2} + 1} + 3$ i.c.	[_linear]	✓

3456	$y^{'} = - \cot (t) y + 6 \cos {(t)}^{2}$ i.c.	[_linear]	✓

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

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

3463	$(- x^{2} + 1) y^{'} + 4 x y = {(- x^{2} + 1)}^{3 / 2}$	[_linear]	✓

3464	$y^{'} - y \cot (x) + \frac{1}{\sin (x)} = 0$	[_linear]	✓

3472	$y^{'} + \frac{x y}{a^{2} + x^{2}} = x$	[_linear]	✓

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

3475	$y^{'} - y \tan (x) = 1$ i.c.	[_linear]	✓

3478	$\sin (x) y^{'} + 2 y \cos (x) = 1$ i.c.	[_linear]	✓

3515	$y^{'} = 2 x y$	[_separable]	✓

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

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

3520	$y^{'} = \frac{2 x (y - 1)}{x^{2} + 3}$	[_separable]	✓

3521	$y - x y^{'} = 3 - 2 x^{2} y^{'}$	[_separable]	✓

3524	$y^{'} = \frac{x^{2} y - 32}{- x^{2} + 16} + 32$	[_linear]	✓

3525	$(x - a) (x - b) y^{'} - y + c = 0$	[_separable]	✓

3527	$(- x^{2} + 1) y^{'} + x y = a x$ i.c.	[_separable]	✓

3530	$y^{'} - y = e^{2 x}$	[[_linear, ‘class A‘]]	✓

3531	$x^{2} y^{'} - 4 x y = x^{7} \sin (x)$	[_linear]	✓

3532	$y^{'} + 2 x y = 2 x^{3}$	[_linear]	✓

3533	$y^{'} + \frac{2 x y}{x^{2} + 1} = 4 x$	[_linear]	✓

3534	$y^{'} + \frac{2 x y}{x^{2} + 1} = \frac{4}{{(x^{2} + 1)}^{2}}$	[_linear]	✓

3535	$2 \cos {(x)}^{2} y^{'} + y \sin (2 x) = 4 \cos {(x)}^{4}$	[_linear]	✓

3536	$y^{'} + \frac{y}{\ln (x) x} = 9 x^{2}$	[_linear]	✓

3537	$y^{'} - y \tan (x) = 8 \sin {(x)}^{3}$	[_linear]	✓

3538	$t x^{'} + 2 x = 4 e^{t}$	[_linear]	✓

3539	$y^{'} = \sin (x) (y \sec (x) - 2)$	[_linear]	✓

3540	$1 - y \sin (x) - \cos (x) y^{'} = 0$	[_linear]	✓

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

3542	$y^{'} + α y = e^{β x}$	[[_linear, ‘class A‘]]	✓

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]	✓

3598	$y^{'} = \frac{2 x (y - 1)}{x^{2} + 3}$	[_separable]	✓

3599	$y - x y^{'} = 3 - 2 x^{2} y^{'}$	[_separable]	✓

3602	$y^{'} = \frac{x^{2} y - 32}{- x^{2} + 16} + 2$	[_separable]	✓

3603	$(x - a) (x - b) y^{'} - y + c = 0$	[_separable]	✓

3605	$(- x^{2} + 1) y^{'} + x y = a x$ i.c.	[_separable]	✓

3610	$y^{'} + y = 4 e^{x}$	[[_linear, ‘class A‘]]	✓

3611	$y^{'} + \frac{2 y}{x} = 5 x^{2}$	[_linear]	✓

3612	$x^{2} y^{'} - 4 x y = x^{7} \sin (x)$	[_linear]	✓

3613	$y^{'} + 2 x y = 2 x^{3}$	[_linear]	✓

3614	$y^{'} + \frac{2 x y}{- x^{2} + 1} = 4 x$	[_linear]	✓

3615	$y^{'} + \frac{2 x y}{x^{2} + 1} = \frac{4}{{(x^{2} + 1)}^{2}}$	[_linear]	✓

3616	$2 \cos {(x)}^{2} y^{'} + y \sin (2 x) = 4 \cos {(x)}^{4}$	[_linear]	✓

3617	$y^{'} + \frac{y}{\ln (x) x} = 9 x^{2}$	[_linear]	✓

3618	$y^{'} - y \tan (x) = 8 \sin {(x)}^{3}$	[_linear]	✓

3619	$t x^{'} + 2 x = 4 e^{t}$	[_linear]	✓

3620	$y^{'} = \sin (x) (y \sec (x) - 2)$	[_linear]	✓

3621	$1 - y \sin (x) - \cos (x) y^{'} = 0$	[_linear]	✓

3622	$y^{'} - \frac{y}{x} = 2 x^{2} \ln (x)$	[_linear]	✓

3623	$y^{'} + α y = e^{β x}$	[[_linear, ‘class A‘]]	✓

3624	$y^{'} + \frac{m y}{x} = \ln (x)$	[_linear]	✓

3625	$y^{'} + \frac{2 y}{x} = 4 x$ i.c.	[_linear]	✓

3626	$\sin (x) y^{'} - y \cos (x) = \sin (2 x)$ i.c.	[_linear]	✓

3627	$x^{'} + \frac{2 x}{4 - t} = 5$ i.c.	[_linear]	✓

3628	$y - e^{x} + y^{'} = 0$ i.c.	[[_linear, ‘class A‘]]	✓

3629	$y^{'} - 2 y = {\begin{array}{cc} 1 & x \leq 1 \\ 0 & 1 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

3630	$y^{'} - 2 y = {\begin{array}{cc} 1 - x & x < 1 \\ 0 & 1 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

3632	$y^{'} + \frac{y}{x} = \cos (x)$	[_linear]	✓

3633	$y^{'} + y = e^{- 2 x}$	[[_linear, ‘class A‘]]	✓

3634	$y^{'} + y \cot (x) = 2 \cos (x)$	[_linear]	✓

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

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

3972	$- y + y^{'} = {\begin{array}{cc} 2 & 0 \leq t < 1 \\ - 1 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

4093	$3 y - 2 x + (3 x - 2) y^{'} = 0$	[_linear]	✓

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

4100	$y^{'} + y = x^{2} + 2$	[[_linear, ‘class A‘]]	✓

4101	$y^{'} - y \tan (x) = x$ i.c.	[_linear]	✓

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

4107	$y^{'} - 3 y = e^{3 x} + e^{- 3 x}$ i.c.	[[_linear, ‘class A‘]]	✓

4109	$x y^{'} + 2 y = (3 x + 2) e^{3 x}$ i.c.	[_linear]	✓

4116	$\cos (x) y^{'} + y \sin (x) = 1$ i.c.	[_linear]	✓

4191	$y^{'} - y = x^{3}$	[[_linear, ‘class A‘]]	✓

4192	$y^{'} + y \cot (x) = x$	[_linear]	✓

4193	$y^{'} + y \cot (x) = \tan (x)$	[_linear]	✓

4194	$y^{'} + y \tan (x) = \cot (x)$	[_linear]	✓

4195	$y^{'} + y \ln (x) = x^{- x}$	[_linear]	✓

4196	$x y^{'} + y = x$	[_linear]	✓

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

4198	$x y^{'} + n y = x^{n}$	[_linear]	✓

4199	$x y^{'} - n y = x^{n}$	[_linear]	✓

4200	$(x^{3} + x) y^{'} + y = x$	[_linear]	✓

4201	$\cot (x) y^{'} + y = x$	[_linear]	✓

4202	$\cot (x) y^{'} + y = \tan (x)$	[_linear]	✓

4203	$\tan (x) y^{'} + y = \cot (x)$	[_linear]	✓

4204	$\tan (x) y^{'} = y - \cos (x)$	[_linear]	✓

4205	$y^{'} + y \cos (x) = \sin (2 x)$	[_linear]	✓

4206	$\cos (x) y^{'} + y = \sin (2 x)$	[_linear]	✓

4207	$y^{'} + y \sin (x) = \sin (2 x)$	[_linear]	✓

4208	$\sin (x) y^{'} + y = \sin (2 x)$	[_linear]	✓

4209	$\sqrt{x^{2} + 1} y^{'} + y = 2 x$	[_linear]	✓

4210	$\sqrt{x^{2} + 1} y^{'} - y = 2 \sqrt{x^{2} + 1}$	[_linear]	✓

4211	$\sqrt{(x + a) (x + b)} (2 y^{'} - 3) + y = 0$	[_linear]	✓

4212	$\sqrt{(x + a) (x + b)} y^{'} + y = \sqrt{x + a} - \sqrt{x + b}$	[_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]	✓

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

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

4227	$y^{'} - 2 x y = 2 x$ 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]	✓

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]	✓

4269	$x y^{'} - 3 y = x^{4}$	[_linear]	✓

4270	$y^{'} + y = \frac{1}{1 + e^{2 x}}$	[_linear]	✓

4271	$(x^{2} + 1) y^{'} + 2 x y = \cot (x)$	[_linear]	✓

4272	$y^{'} + y = 2 x e^{- x} + x^{2}$	[[_linear, ‘class A‘]]	✓

4273	$y^{'} + y \cot (x) = 2 x \csc (x)$	[_linear]	✓

4274	$2 y - x^{3} = x y^{'}$	[_linear]	✓

4280	$x y^{'} + y = x \cos (x)$	[_linear]	✓

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

4284	$x y^{'} + y = x^{2} \cos (x)$	[_linear]	✓

4289	$y^{'} + 2 x y = e^{- x^{2}}$	[_linear]	✓

4291	$(x^{2} + 1) y^{'} + 2 x y = 4 x^{3}$	[_linear]	✓

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

4297	$\ln (x) y^{'} + \frac{x + y}{x} = 0$	[_linear]	✓

4359	$1 + y \cos (x) - \sin (x) y^{'} = 0$	[_linear]	✓

4367	$(2 x + 3) y^{'} = y + \sqrt{2 x + 3}$	[_linear]	✓

4369	$y^{'} = 1 + 3 y \tan (x)$	[_linear]	✓

4370	$(\cos (x) + 1) y^{'} = \sin (x) (\sin (x) + \sin (x) \cos (x) - y)$	[_linear]	✓

4371	$y^{'} = (\sin {(x)}^{2} - y) \cos (x)$	[_linear]	✓

4372	$(x + 1) y^{'} - y = x {(x + 1)}^{2}$	[_linear]	✓

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

4404	$y - 1 - x y + x y^{'} = 0$	[_linear]	✓

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

4437	$y \sin (x) + \cos {(x)}^{2} - \cos (x) y^{'} = 0$	[_linear]	✓

4440	$(\cos (x) + 1) y^{'} + \sin (x) (\sin (x) + \sin (x) \cos (x) - y) = 0$	[_linear]	✓

4609	$y^{'} = x + \sin (x) + y$	[[_linear, ‘class A‘]]	✓

4610	$y^{'} = x^{2} + 3 \cosh (x) + 2 y$	[[_linear, ‘class A‘]]	✓

4611	$y^{'} = a + b x + c y$	[[_linear, ‘class A‘]]	✓

4612	$y^{'} = a \cos (b x + c) + k y$	[[_linear, ‘class A‘]]	✓

4613	$y^{'} = a \sin (b x + c) + k y$	[[_linear, ‘class A‘]]	✓

4614	$y^{'} = a + b e^{k x} + c y$	[[_linear, ‘class A‘]]	✓

4615	$y^{'} = x (x^{2} - y)$	[_linear]	✓

4616	$y^{'} = x (e^{- x^{2}} + a y)$	[_linear]	✓

4617	$y^{'} = x^{2} (a x^{3} + b y)$	[_linear]	✓

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

4619	$y^{'} = \sin (x) \cos (x) + y \cos (x)$	[_linear]	✓

4620	$y^{'} = e^{\sin (x)} + y \cos (x)$	[_linear]	✓

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

4622	$y^{'} = 1 - y \cot (x)$	[_linear]	✓

4623	$y^{'} = x \csc (x) - y \cot (x)$	[_linear]	✓

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

4625	$y^{'} = \sec (x) - y \cot (x)$	[_linear]	✓

4626	$y^{'} = e^{x} \sin (x) + y \cot (x)$	[_linear]	✓

4627	$y^{'} + \csc (x) + 2 y \cot (x) = 0$	[_linear]	✓

4628	$y^{'} = 4 \csc (x) x \sec {(x)}^{2} - 2 y \cot (2 x)$	[_linear]	✓

4629	$y^{'} = 2 \cot {(x)}^{2} \cos (2 x) - 2 y \csc (2 x)$	[_linear]	✓

4630	$y^{'} = 4 \csc (x) x (\sin {(x)}^{3} + y)$	[_linear]	✓

4631	$y^{'} = 4 \csc (x) x (1 - \tan {(x)}^{2} + y)$	[_linear]	✓

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

4633	$y^{'} + \tan (x) = (1 - y) \sec (x)$	[_linear]	✓

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

4635	$y^{'} = \cos (x) + y \tan (x)$	[_linear]	✓

4636	$y^{'} = \cos (x) - y \tan (x)$	[_linear]	✓

4637	$y^{'} = \sec (x) - y \tan (x)$	[_linear]	✓

4638	$y^{'} = \sin (2 x) + y \tan (x)$	[_linear]	✓

4639	$y^{'} = \sin (2 x) - y \tan (x)$	[_linear]	✓

4640	$y^{'} = \sin (x) + 2 y \tan (x)$	[_linear]	✓

4641	$y^{'} = 2 + 2 \sec (2 x) + 2 y \tan (2 x)$	[_linear]	✓

4642	$y^{'} = \csc (x) + 3 y \tan (x)$	[_linear]	✓

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

4644	$y^{'} = 6 e^{2 x} - y \tanh (x)$	[_linear]	✓

4645	$y^{'} = f (x) f^{'} (x) + f^{'} (x) y$	[_linear]	✓

4646	$y^{'} = f (x) + g (x) y$	[_linear]	✓

4679	$y^{'} = \sin (x) (2 \sec {(x)}^{2} - y)$	[_linear]	✓

4681	$y^{'} = y \sec (x) + {(\sin (x) - 1)}^{2}$	[_linear]	✓

4738	$y^{'} = \sec {(x)}^{2} + y \sec (x) Csx (x)$	[_linear]	✓

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

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

4745	$x y^{'} = x^{3} - y$	[_linear]	✓

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

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

4748	$x y^{'} = x \sin (x) - y$	[_linear]	✓

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

4750	$x y^{'} = x^{n} \ln (x) - y$	[_linear]	✓

4751	$x y^{'} = \sin (x) - 2 y$	[_linear]	✓

4752	$x y^{'} = a y$	[_separable]	✓

4753	$x y^{'} = 1 + x + a y$	[_linear]	✓

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

4755	$x y^{'} = a x^{2} + b y$	[_linear]	✓

4756	$x y^{'} = a + b x^{n} + c y$	[_linear]	✓

4757	$x y^{'} + 2 + (3 - x) y = 0$	[_linear]	✓

4758	$x y^{'} + x + (a x + 2) y = 0$	[_linear]	✓

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

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

4761	$x y^{'} = a x - (- b x^{2} + 1) y$	[_linear]	✓

4762	$x y^{'} + x + (- a x^{2} + 2) y = 0$	[_linear]	✓

4821	$(x + 1) y^{'} = x^{3} (4 + 3 x) + y$	[_linear]	✓

4822	$(x + 1) y^{'} = {(x + 1)}^{4} + 2 y$	[_linear]	✓

4823	$(x + 1) y^{'} = e^{x} {(x + 1)}^{n + 1} + n y$	[_linear]	✓

4829	$(x + a) y^{'} = b x + y$	[_linear]	✓

4830	$(x + a) y^{'} + b x^{2} + y = 0$	[_linear]	✓

4831	$(x + a) y^{'} = 2 {(x + a)}^{5} + 3 y$	[_linear]	✓

4832	$(x + a) y^{'} = b + c y$	[_separable]	✓

4833	$(x + a) y^{'} = b x + c y$	[_linear]	✓

4836	$2 x y^{'} = 2 x^{3} - y$	[_linear]	✓

4842	$(1 - 2 x) y^{'} = 16 + 32 x - 6 y$	[_linear]	✓

4844	$2 (1 - x) y^{'} = 4 x \sqrt{1 - x} + y$	[_linear]	✓

4849	$x^{2} y^{'} = - y + a$	[_separable]	✓

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

4851	$x^{2} y^{'} = a + b x + c x^{2} - x y$	[_linear]	✓

4852	$x^{2} y^{'} + (1 - 2 x) y = x^{2}$	[_linear]	✓

4853	$x^{2} y^{'} = a + b x y$	[_linear]	✓

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

4855	$x^{2} y^{'} + x (x + 2) y = x (1 - e^{- 2 x}) - 2$	[_linear]	✓

4856	$x^{2} y^{'} + 2 x (1 - x) y = e^{x} (2 e^{x} - 1)$	[_linear]	✓

4877	$(- x^{2} + 1) y^{'} = 1 - x^{2} + y$	[_linear]	✓

4878	$(- x^{2} + 1) y^{'} + 1 = x y$	[_linear]	✓

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

4880	$(x^{2} + 1) y^{'} + a + x y = 0$	[_linear]	✓

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

4882	$(- x^{2} + 1) y^{'} + a - x y = 0$	[_linear]	✓

4883	$(- x^{2} + 1) y^{'} - x + x y = 0$	[_separable]	✓

4884	$(- x^{2} + 1) y^{'} - x^{2} + x y = 0$	[_linear]	✓

4885	$(- x^{2} + 1) y^{'} + x^{2} + x y = 0$	[_linear]	✓

4886	$(x^{2} + 1) y^{'} = x (x^{2} + 1) - x y$	[_linear]	✓

4887	$(x^{2} + 1) y^{'} = x (3 x^{2} - y)$	[_linear]	✓

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

4889	$(x^{2} + 1) y^{'} = 2 x (x - y)$	[_linear]	✓

4890	$(x^{2} + 1) y^{'} = 2 x {(x^{2} + 1)}^{2} + 2 x y$	[_linear]	✓

4891	$(- x^{2} + 1) y^{'} + \cos (x) = 2 x y$	[_linear]	✓

4892	$(x^{2} + 1) y^{'} = \tan (x) - 2 x y$	[_linear]	✓

4893	$(- x^{2} + 1) y^{'} = a + 4 x y$	[_linear]	✓

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

4903	$(x^{2} + 1) y^{'} = 1 + x^{2} - y arccot (x)$	[_linear]	✓

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

4906	$(a^{2} + x^{2}) y^{'} = (b + y) (x + \sqrt{a^{2} + x^{2}})$	[_separable]	✓

4910	$x (1 - x) y^{'} = a + (x + 1) y$	[_linear]	✓

4911	$x (1 - x) y^{'} = 2 + 2 x y$	[_linear]	✓

4912	$x (1 - x) y^{'} = 2 x y - 2$	[_linear]	✓

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

4914	$x (1 - x) y^{'} + (2 x + 1) y = a$	[_linear]	✓

4915	$x (1 - x) y^{'} = a + 2 (2 - x) y$	[_linear]	✓

4916	$x (1 - x) y^{'} + 2 - 3 x y + y = 0$	[_linear]	✓

4917	$x (x + 1) y^{'} = (x + 1) (x^{2} - 1) + (x^{2} + x - 1) y$	[_linear]	✓

4918	$(- 2 + x) (x - 3) y^{'} + x^{2} - 8 y + 3 x y = 0$	[_linear]	✓

4920	${(x + a)}^{2} y^{'} = 2 (x + a) (b + y)$	[_separable]	✓

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

4923	$(x - a) (x - b) y^{'} = (x - a) (x - b) + (2 x - a - b) y$	[_linear]	✓

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

4928	$2 x^{2} y^{'} + x \cot (x) - 1 + 2 x^{2} y \cot (x) = 0$	[_linear]	✓

4931	$2 (- x^{2} + 1) y^{'} = \sqrt{- x^{2} + 1} + (x + 1) y$	[_linear]	✓

4932	$x (1 - 2 x) y^{'} + 1 + (1 - 4 x) y = 0$	[_linear]	✓

4934	$2 x (1 - x) y^{'} + x + (1 - 2 x) y = 0$	[_linear]	✓

4936	$2 (x^{2} + x + 1) y^{'} = 1 + 8 x^{2} - (2 x + 1) y$	[_linear]	✓

4937	$4 (x^{2} + 1) y^{'} - 4 x y - x^{2} = 0$	[_linear]	✓

4941	$x (a x + 1) y^{'} + a - y = 0$	[_separable]	✓

4943	$x^{3} y^{'} = a + b x^{2} y$	[_linear]	✓

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

4953	$x (x^{2} + 1) y^{'} = a x^{2} + y$	[_linear]	✓

4954	$x (- x^{2} + 1) y^{'} = a x^{2} + y$	[_linear]	✓

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

4956	$x (x^{2} + 1) y^{'} = a - x^{2} y$	[_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]	✓

4960	$x (- x^{2} + 1) y^{'} = x^{3} (- x^{2} + 1) + (- 2 x^{2} + 1) y$	[_linear]	✓

4961	$x (x^{2} + 1) y^{'} = 2 - 4 x^{2} y$	[_linear]	✓

4962	$x (x^{2} + 1) y^{'} = x - (5 x^{2} + 3) y$	[_linear]	✓

4973	$x (- x^{3} + 1) y^{'} = 2 x - (- 4 x^{3} + 1) y$	[_linear]	✓

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

4978	$x^{5} y^{'} = 1 - 3 x^{4} y$	[_linear]	✓

4981	$x^{n} y^{'} = a + b x^{n - 1} y$	[_linear]	✓

4987	$\sqrt{x^{2} + 1} y^{'} = 2 x - y$	[_linear]	✓

4990	$y^{'} \sqrt{a^{2} + x^{2}} + x + y = \sqrt{a^{2} + x^{2}}$	[_linear]	✓

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]	✓

5012	$(a 0 + a 1 \sin {(x)}^{2}) y^{'} + a 2 x (a 3 + a 1 \sin {(x)}^{2}) + a 1 y \sin (2 x) = 0$	[_linear]	✓

5013	$(x - e^{x}) y^{'} + x e^{x} + (1 - e^{x}) y = 0$	[_linear]	✓

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

5036	$1 - y^{'} = x + y$	[[_linear, ‘class A‘]]	✓

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

5345	${y^{'}}^{2} = y^{2} x^{2}$	[_separable]	✓

5391	${y^{'}}^{2} + y y^{'} = (x + y) x$	[_quadrature]	✓

5404	${y^{'}}^{2} - (2 x y + 1) y^{'} + 2 x y = 0$	[_quadrature]	✓

5406	${y^{'}}^{2} - (x - y) y y^{'} - x y^{3} = 0$	[_separable]	✓

5409	${y^{'}}^{2} - x y (x^{2} + y^{2}) y^{'} + x^{4} y^{4} = 0$	[_separable]	✓

5411	${y^{'}}^{2} + 2 y y^{'} \cot (x) - y^{2} = 0$	[_separable]	✓

5451	$x {y^{'}}^{2} - (2 x + 3 y) y^{'} + 6 y = 0$	[_quadrature]	✓

5455	$x {y^{'}}^{2} + (1 - x) y y^{'} - y^{2} = 0$	[_quadrature]	✓

5456	$x {y^{'}}^{2} + (1 - x^{2} y) y^{'} - x y = 0$	[_quadrature]	✓

5476	$x^{2} {y^{'}}^{2} - x y^{'} + y (1 - y) = 0$	[_separable]	✓

5501	$(a^{2} - x^{2}) {y^{'}}^{2} - 2 x y y^{'} - y^{2} = 0$	[_separable]	✓

5503	$4 x^{2} {y^{'}}^{2} - 4 x y y^{'} = 8 x^{3} - y^{2}$	[_linear]	✓

5615	${y^{'}}^{3} - (2 x + y^{2}) {y^{'}}^{2} + (x^{2} - y^{2} + 2 x y^{2}) y^{'} - (x^{2} - y^{2}) y^{2} = 0$	[_quadrature]	✓

5616	${y^{'}}^{3} - (y^{2} + x y + x^{2}) {y^{'}}^{2} + x y (y^{2} + x y + x^{2}) y^{'} - x^{3} y^{3} = 0$	[_quadrature]	✓

5624	$x {y^{'}}^{3} - (x + x^{2} + y) {y^{'}}^{2} + (x^{2} + y + x y) y^{'} - x y = 0$	[_quadrature]	✓

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

5692	$y^{'} - \frac{2 y}{x + 1} = {(x + 1)}^{2}$	[_linear]	✓

5712	$y^{'} + \frac{x y}{x^{2} + 1} = \frac{1}{2 x (x^{2} + 1)}$	[_linear]	✓

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

5714	$y^{'} + \frac{y}{{(- x^{2} + 1)}^{3 / 2}} = \frac{x + \sqrt{- x^{2} + 1}}{{(- x^{2} + 1)}^{2}}$	[_linear]	✓

5715	$y^{'} + y \cos (x) = \frac{\sin (2 x)}{2}$	[_linear]	✓

5716	$(x^{2} + 1) y^{'} + y = \arctan (x)$	[_linear]	✓

5770	$\frac{y - x y^{'}}{y^{2} + y^{'}} = \frac{y - x y^{'}}{1 + x^{2} y^{'}}$	[_separable]	✓

5791	$7 y - 3 + (2 x + 1) y^{'} = 0$	[_separable]	✓

5839	$x y^{'} + y = x^{3}$	[_linear]	✓

5842	$x^{'} + 2 x y = e^{- y^{2}}$	[_linear]	✓

5843	$r^{'} = (r + e^{- θ}) \tan (θ)$	[_linear]	✓

5844	$y^{'} - \frac{2 x y}{x^{2} + 1} = 1$	[_linear]	✓

5847	$\tan (θ) r^{'} - r = \tan {(θ)}^{2}$	[_linear]	✓

5848	$2 y + y^{'} = 3 e^{- 2 x}$	[[_linear, ‘class A‘]]	✓

5849	$2 y + y^{'} = \frac{3 e^{- 2 x}}{4}$	[[_linear, ‘class A‘]]	✓

5850	$2 y + y^{'} = \sin (x)$	[[_linear, ‘class A‘]]	✓

5851	$y^{'} + y \cos (x) = e^{2 x}$	[_linear]	✓

5852	$y^{'} + y \cos (x) = \frac{\sin (2 x)}{2}$	[_linear]	✓

5853	$x y^{'} + y = x \sin (x)$	[_linear]	✓

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

5858	$y^{'} - y = e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓

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

5881	$y^{'} + a y = k e^{b x}$	[[_linear, ‘class A‘]]	✓

5885	$y^{'} + a y = b \sin (k x)$	[[_linear, ‘class A‘]]	✓

5889	$y^{'} + y \cos (x) = e^{- \sin (x)}$	[_linear]	✓

5892	$x y^{'} + a y + b x^{n} = 0$	[_linear]	✓

5897	$(x^{2} - 1) y^{'} + 2 x y - \cos (x) = 0$	[_linear]	✓

5902	$\cos (x) y^{'} + y + (\sin (x) + 1) \cos (x) = 0$	[_linear]	✓

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

6029	$y^{'} = e^{a x} + a y$	[[_linear, ‘class A‘]]	✓

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

6102	$y^{'} - x y = x$ i.c.	[_separable]	✓

6105	$y^{'} + y = e^{x}$	[[_linear, ‘class A‘]]	✓

6106	$x^{2} y^{'} + 3 x y = 1$	[_linear]	✓

6107	$y^{'} + 2 x y - x e^{- x^{2}} = 0$	[_linear]	✓

6108	$2 x y^{'} + y = 2 x^{5 / 2}$	[_linear]	✓

6109	$\cos (x) y^{'} + y = \cos {(x)}^{2}$	[_linear]	✓

6110	$y^{'} + \frac{y}{\sqrt{x^{2} + 1}} = \frac{1}{x + \sqrt{x^{2} + 1}}$	[_linear]	✓

6111	$(e^{x} + 1) y^{'} + 2 y e^{x} = (e^{x} + 1) e^{x}$	[_linear]	✓

6112	$x \ln (x) y^{'} + y = \ln (x)$	[_linear]	✓

6113	$(- x^{2} + 1) y^{'} = x y + 2 x \sqrt{- x^{2} + 1}$	[_linear]	✓

6114	$y^{'} + y \tanh (x) = 2 e^{x}$	[_linear]	✓

6115	$y^{'} + y \cos (x) = \sin (2 x)$	[_linear]	✓

6116	$x^{'} = \cos (y) - x \tan (y)$	[_linear]	✓

6117	$x^{'} + x - e^{y} = 0$	[[_linear, ‘class A‘]]	✓

6118	$x^{'} = \frac{3 y^{2 / 3} - x}{3 y}$	[_linear]	✓

6131	$(- 1 + x) y^{'} + y - \frac{1}{x^{2}} + \frac{2}{x^{3}} = 0$	[_linear]	✓

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

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

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

6230	$\sin (θ) \cos (θ) r^{'} - \sin {(θ)}^{2} = r \cos {(θ)}^{2}$	[_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]	✓

6273	$y^{'} = x^{3} (1 - y)$ i.c.	[_separable]	✓

6280	$y^{'} = x^{2} (y + 1)$ i.c.	[_separable]	✓

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

6294	$x^{2} y^{'} + \sin (x) - y = 0$	[_linear]	✓

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

6297	$3 t = e^{t} y^{'} + \ln (t) y$	[_linear]	✓

6299	$3 r = r^{'} - θ^{3}$	[[_linear, ‘class A‘]]	✓

6300	$y^{'} - y - e^{3 x} = 0$	[[_linear, ‘class A‘]]	✓

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

6302	$r^{'} + r \tan (θ) = \sec (θ)$	[_linear]	✓

6303	$x y^{'} + 2 y = \frac{1}{x^{3}}$	[_linear]	✓

6304	$t + y + 1 - y^{'} = 0$	[[_linear, ‘class A‘]]	✓

6305	$y^{'} = x^{2} e^{- 4 x} - 4 y$	[[_linear, ‘class A‘]]	✓

6306	$x^{'} y + 2 x = 5 y^{3}$	[_linear]	✓

6307	$x y^{'} + 3 x^{2} + 3 y = \frac{\sin (x)}{x}$	[_linear]	✓

6308	$(x^{2} + 1) y^{'} + x y - x = 0$	[_separable]	✓

6309	$(- x^{2} + 1) y^{'} - x^{2} y = (x + 1) \sqrt{- x^{2} + 1}$	[_linear]	✓

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

6311	$y^{'} + 4 y - e^{- x} = 0$ i.c.	[[_linear, ‘class A‘]]	✓

6312	$t^{2} x^{'} + 3 t x = t^{4} \ln (t) + 1$ i.c.	[_linear]	✓

6313	$y^{'} + \frac{3 y}{x} + 2 = 3 x$ i.c.	[_linear]	✓

6314	$\cos (x) y^{'} + y \sin (x) = 2 x \cos {(x)}^{2}$ i.c.	[_linear]	✓

6315	$\sin (x) y^{'} + y \cos (x) = x \sin (x)$ i.c.	[_linear]	✓

6319	$y^{'} + \frac{3 y}{x} = x^{2}$	[_linear]	✓

6320	$x^{'} = α - β \cos (\frac{π t}{12}) - k x$ i.c.	[[_linear, ‘class A‘]]	✓

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

6323	$x^{10 / 3} - 2 y + x y^{'} = 0$	[_linear]	✓

6340	$y^{'} - 4 y = 32 x^{2}$	[[_linear, ‘class A‘]]	✓

6342	$y^{'} + \frac{3 y}{x} = x^{2} - 4 x + 3$	[_linear]	✓

6398	$y^{'} - y = e^{2 x}$	[[_linear, ‘class A‘]]	✓

6399	$x^{2} y^{'} + 2 x y - x + 1 = 0$ i.c.	[_linear]	✓

6400	$y^{'} + y = {(x + 1)}^{2}$ i.c.	[[_linear, ‘class A‘]]	✓

6401	$2 x y + x^{2} y^{'} = \sinh (x)$ i.c.	[_linear]	✓

6402	$y^{'} + \frac{y}{1 - x} + 2 x - x^{2} = 0$	[_linear]	✓

6403	$y^{'} + \frac{y}{1 - x} + x - x^{2} = 0$	[_linear]	✓

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

6415	$y^{'} - \frac{2 y}{x} - x^{2} = 0$	[_linear]	✓

6416	$y^{'} + \frac{2 y}{x} - x^{3} = 0$	[_linear]	✓

6420	$2 y + y^{'} = e^{3 x}$	[[_linear, ‘class A‘]]	✓

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

6425	$(x^{2} - 1) y^{'} + 2 x y = x$	[_separable]	✓

6426	$y^{'} + y \tanh (x) = 2 \sinh (x)$	[_linear]	✓

6427	$x y^{'} - 2 y = x^{3} \cos (x)$	[_linear]	✓

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

6440	$- y + x y^{'} = x^{3} + 3 x^{2} - 2 x$	[_linear]	✓

6441	$y^{'} + y \tan (x) = \sin (x)$	[_linear]	✓

6442	$- y + x y^{'} = x^{3} \cos (x)$ i.c.	[_linear]	✓

6443	$(x^{2} + 1) y^{'} + 3 x y = 5 x$ i.c.	[_separable]	✓

6444	$y^{'} + y \cot (x) = 5 e^{\cos (x)}$ i.c.	[_linear]	✓

6455	$(- x^{2} + 1) y^{'} = 1 + x y$	[_linear]	✓

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

6460	$y^{'} - y \tan (x) = \cos (x) - 2 x \sin (x)$ i.c.	[_linear]	✓

6462	$(x^{2} + 1) y^{'} = x (y + 1)$	[_separable]	✓

6463	$x y^{'} + 2 y = 3 x - 1$ i.c.	[_linear]	✓

6466	$y^{'} + \frac{y}{x} = \sin (2 x)$ i.c.	[_linear]	✓

6470	$(- x^{3} + 1) y^{'} + x^{2} y = x^{2} (- x^{3} + 1)$	[_linear]	✓

6471	$y^{'} + \frac{y}{x} = \sin (x)$ i.c.	[_linear]	✓

6473	$y^{'} + (\frac{1}{x} - \frac{2 x}{- x^{2} + 1}) y = \frac{1}{- x^{2} + 1}$	[_linear]	✓

6474	$(x^{2} + 1) y^{'} + x y = {(x^{2} + 1)}^{3 / 2}$	[_linear]	✓

6477	$y^{'} + y \cot (x) = \cos (x)$ i.c.	[_linear]	✓

6515	$y^{'} - 5 y = (- 1 + x) \sin (x) + (x + 1) \cos (x)$	[[_linear, ‘class A‘]]	✓

6516	$y^{'} - 5 y = 3 e^{x} - 2 x + 1$	[[_linear, ‘class A‘]]	✓

6517	$y^{'} - 5 y = x^{2} e^{x} - x e^{5 x}$	[[_linear, ‘class A‘]]	✓

6523	$y^{'} - y = e^{x}$	[[_linear, ‘class A‘]]	✓

6524	$y^{'} - y = x e^{2 x} + 1$	[[_linear, ‘class A‘]]	✓

6525	$y^{'} - y = \sin (x) + \cos (2 x)$	[[_linear, ‘class A‘]]	✓

6533	$y^{'} + \frac{4 y}{x} = x^{4}$	[_linear]	✓

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

6569	$x y^{'} = 2 y$	[_separable]	✓

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

6580	$1 + 2 y + (- x^{2} + 4) y^{'} = 0$	[_separable]	✓

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

6588	$1 + 2 y - (4 - x) y^{'} = 0$	[_separable]	✓

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

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

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

6642	$y^{'} - y = x y$	[_separable]	✓

6643	$- 3 y - (- 2 + x) e^{x} + x y^{'} = 0$	[_linear]	✓

6644	$i^{'} - 6 i = 10 \sin (2 t)$	[[_linear, ‘class A‘]]	✓

6649	$r^{'} + 2 r \cos (θ) + \sin (2 θ) = 0$	[_linear]	✓

6654	$x y^{'} = y (1 - x \tan (x)) + x^{2} \cos (x)$	[_linear]	✓

6659	$x y^{'} = 2 y + x^{3} e^{x}$ i.c.	[_linear]	✓

6660	$L i^{'} + R i = E \sin (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓

6667	$x {y^{'}}^{2} + (y - 1 - x^{2}) y^{'} - x (y - 1) = 0$	[_quadrature]	✓

6794	$x y^{'} = 1 - x + 2 y$	[_linear]	✓

6842	$y^{'} + x y = \frac{1}{x^{3}}$	[_linear]	✓

6897	$y^{'} + 4 x y = 8 x^{3}$	[_linear]	✓

6900	$x y^{'} - 3 x y = 1$	[[_linear, ‘class A‘]]	✓

6901	$2 x y^{'} - y = 2 x \cos (x)$	[_linear]	✓

6902	$x y + x^{2} y^{'} = 10 \sin (x)$	[_linear]	✓

6903	$y^{'} + 2 x y = 1$	[_linear]	✓

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

6914	$3 x y^{'} + 5 y = 10$	[_separable]	✓

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

6951	$x y^{'} = y$	[_separable]	✓

6952	$y^{'} - y = x$	[[_linear, ‘class A‘]]	✓

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

6977	$y^{'} = x - 2 y$ i.c.	[[_linear, ‘class A‘]]	✓

6980	$2 y + y^{'} = 3 x - 6$	[[_linear, ‘class A‘]]	✓

6985	$x y^{'} = y$	[_separable]	✓

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

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

7000	$y^{'} + y \sin (x) = x$	[_linear]	✓

7001	$y^{'} - 2 x y = e^{x}$	[_linear]	✓

7009	$2 y + y^{'} = 3 x$	[[_linear, ‘class A‘]]	✓

7022	$y^{'} = 1 - x y$ i.c.	[_linear]	✓

7023	$y^{'} = 1 - x y$ i.c.	[_linear]	✓

7024	$y^{'} = 1 - x y$ i.c.	[_linear]	✓

7025	$y^{'} = 1 - x y$ i.c.	[_linear]	✓

7032	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓

7033	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓

7038	$y^{'} = \frac{x^{2}}{5} + y$ i.c.	[[_linear, ‘class A‘]]	✓

7039	$y^{'} = \frac{x^{2}}{5} + y$ i.c.	[[_linear, ‘class A‘]]	✓

7042	$y^{'} = y - \cos (\frac{π x}{2})$ i.c.	[[_linear, ‘class A‘]]	✓

7043	$y^{'} = y - \cos (\frac{π x}{2})$ i.c.	[[_linear, ‘class A‘]]	✓

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

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

7046	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓

7049	$y^{'} = x^{2} - 2 y$	[[_linear, ‘class A‘]]	✓

7067	$x y^{'} = 4 y$	[_separable]	✓

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]	✓

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

7147	$y^{'} + y = e^{3 x}$	[[_linear, ‘class A‘]]	✓

7149	$y^{'} + 3 x^{2} y = x^{2}$	[_separable]	✓

7150	$y^{'} + 2 x y = x^{3}$	[_linear]	✓

7151	$x y + x^{2} y^{'} = 1$	[_linear]	✓

7152	$y^{'} = 2 y + x^{2} + 5$	[[_linear, ‘class A‘]]	✓

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

7154	$x y^{'} + 2 y = 3$	[_separable]	✓

7155	$4 y + x y^{'} = x^{3} - x$	[_linear]	✓

7156	$(x + 1) y^{'} - x y = x^{2} + x$	[_linear]	✓

7157	$x^{2} y^{'} + x (x + 2) y = e^{x}$	[_linear]	✓

7158	$x y^{'} + (x + 1) y = e^{- x} \sin (2 x)$	[_linear]	✓

7161	$\cos (x) y^{'} + y \sin (x) = 1$	[_linear]	✓

7162	$\cos {(x)}^{2} \sin (x) y^{'} + \cos {(x)}^{3} y = 1$	[_linear]	✓

7163	$(x + 1) y^{'} + (x + 2) y = 2 x e^{- x}$	[_linear]	✓

7164	${(x + 2)}^{2} y^{'} = 5 - 8 y - 4 x y$	[_linear]	✓

7165	$r^{'} + r \sec (t) = \cos (t)$	[_linear]	✓

7166	$p^{'} + 2 t p = p + 4 t - 2$	[_separable]	✓

7167	$x y^{'} + (3 x + 1) y = e^{- 3 x}$	[_linear]	✓

7168	$(x^{2} - 1) y^{'} + 2 y = {(x + 1)}^{2}$	[_linear]	✓

7169	$y^{'} = x + 5 y$ i.c.	[[_linear, ‘class A‘]]	✓

7170	$y^{'} = 2 x - 3 y$ i.c.	[[_linear, ‘class A‘]]	✓

7171	$x y^{'} + y = e^{x}$ i.c.	[_linear]	✓

7175	$x y^{'} + y = 4 x + 1$ i.c.	[_linear]	✓

7176	$y^{'} + 4 x y = x^{3} e^{x^{2}}$ i.c.	[_linear]	✓

7177	$(x + 1) y^{'} + y = \ln (x)$ i.c.	[_linear]	✓

7178	$x (x + 1) y^{'} + x y = 1$ i.c.	[_linear]	✓

7179	$y^{'} - y \sin (x) = 2 \sin (x)$ i.c.	[_separable]	✓

7180	$y^{'} + y \tan (x) = \cos {(x)}^{2}$ i.c.	[_linear]	✓

7181	$2 y + y^{'} = {\begin{array}{cc} 1 & 0 \leq x \leq 3 \\ 0 & 3 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

7182	$y^{'} + y = {\begin{array}{cc} 1 & 0 \leq x \leq 1 \\ - 1 & 1 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

7183	$y^{'} + 2 x y = {\begin{array}{cc} x & 0 \leq x < 1 \\ 0 & 1 \leq x \end{array}$ i.c.	[_linear]	✓

7184	$(x^{2} + 1) y^{'} + 2 x y = {\begin{array}{cc} x & 0 \leq x < 1 \\ - x & 1 \leq x \end{array}$ i.c.	[_linear]	✓

7185	$y^{'} + ({\begin{array}{cc} 2 & 0 \leq x \leq 1 \\ - \frac{2}{x} & 1 < x \end{array}) y = 4 x$ i.c.	[_linear]	✓

7186	$y^{'} + ({\begin{array}{cc} 1 & 0 \leq x \leq 2 \\ 5 & 2 < x \end{array}) y = 0$ i.c.	[_separable]	✓

7187	$y^{'} - 2 x y = 1$ i.c.	[_linear]	✓

7188	$y^{'} - 2 x y = - 1$ i.c.	[_linear]	✓

7189	$y^{'} + y e^{x} = 1$ i.c.	[_linear]	✓

7190	$x^{2} y^{'} - y = x^{3}$ i.c.	[_linear]	✓

7191	$x^{3} y^{'} + 2 x^{2} y = 10 \sin (x)$ i.c.	[_linear]	✓

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

7195	$x y^{'} - 4 y = x^{6} e^{x}$ i.c.	[_linear]	✓

7197	$x y^{'} - 4 y = x^{6} e^{x}$ i.c.	[_linear]	✓

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

7401	$y^{'} = (y - 1) (x + 1)$	[_separable]	✓

7408	$y^{'} - y = 2 x - 3$	[[_linear, ‘class A‘]]	✓

7410	$y^{'} + y = 2 x + 1$	[[_linear, ‘class A‘]]	✓

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

7439	$y^{'} (y^{'} + y) = (x + y) x$ i.c.	[_quadrature]	✓

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

7446	$x y^{'} = x + \frac{y}{2}$ i.c.	[_linear]	✓

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

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

7584	$y^{'} + y \cos (x) = \sin (x) \cos (x)$	[_linear]	✓

7592	$y^{'} + y = e^{x}$	[[_linear, ‘class A‘]]	✓

7593	$y^{'} - 2 y = x^{2} + x$	[[_linear, ‘class A‘]]	✓

7594	$3 y^{'} + y = 2 e^{- x}$	[[_linear, ‘class A‘]]	✓

7595	$y^{'} + 3 y = e^{i x}$	[[_linear, ‘class A‘]]	✓

7596	$y^{'} + i y = x$	[[_linear, ‘class A‘]]	✓

7598	$L y^{'} + R y = E \sin (ω x)$ i.c.	[[_linear, ‘class A‘]]	✓

7599	$L y^{'} + R y = E e^{i ω x}$ i.c.	[[_linear, ‘class A‘]]	✓

7600	$y^{'} + a y = b (x)$	[[_linear, ‘class A‘]]	✓

7601	$y^{'} + 2 x y = x$	[_separable]	✓

7602	$x y^{'} + y = 3 x^{3} - 1$	[_linear]	✓

7603	$y^{'} + y e^{x} = 3 e^{x}$	[_separable]	✓

7604	$y^{'} - y \tan (x) = e^{\sin (x)}$	[_linear]	✓

7605	$y^{'} + 2 x y = x e^{- x^{2}}$	[_linear]	✓

7606	$y^{'} + y \cos (x) = e^{- \sin (x)}$ i.c.	[_linear]	✓

7607	$2 x y + x^{2} y^{'} = 1$	[_linear]	✓

7608	$2 y + y^{'} = b (x)$	[[_linear, ‘class A‘]]	✓

7731	$y^{'} = x^{2} y$	[_separable]	✓

7774	$x y^{'} = 2 y$	[_separable]	✓

7803	$y^{'} = 2 x y + 1$	[_linear]	✓

7808	$y^{'} = 4 x y$	[_separable]	✓

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

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

7818	$x^{2} y^{'} = y$ i.c.	[_separable]	✓

7825	$y^{'} - x y = 0$	[_separable]	✓

7826	$y^{'} + x y = x$	[_separable]	✓

7827	$y^{'} + y = \frac{1}{1 + e^{2 x}}$	[_linear]	✓

7828	$y^{'} + y = 2 x e^{- x} + x^{2}$	[[_linear, ‘class A‘]]	✓

7829	$2 y - x^{3} = x y^{'}$	[_linear]	✓

7830	$y^{'} + 2 x y = 0$	[_separable]	✓

7831	$x y^{'} - 3 y = x^{4}$	[_linear]	✓

7832	$(x^{2} + 1) y^{'} + 2 x y = \cot (x)$	[_linear]	✓

7833	$y^{'} + y \cot (x) = 2 x \csc (x)$	[_linear]	✓

7834	$y - x + x y \cot (x) + x y^{'} = 0$	[_linear]	✓

7835	$y^{'} - x y = 0$ i.c.	[_separable]	✓

7836	$y^{'} - 2 x y = 6 x e^{x^{2}}$ i.c.	[_linear]	✓

7838	$y^{'} - \frac{y}{x} = x^{2}$ i.c.	[_linear]	✓

7839	$y^{'} + 4 y = e^{- x}$ i.c.	[[_linear, ‘class A‘]]	✓

7840	$x y + x^{2} y^{'} = 2 x$ i.c.	[_separable]	✓

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

7849	$y^{'} \sin (2 x) = 2 y + 2 \cos (x)$	[_linear]	✓

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

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

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

7885	$2 x + 3 y - 1 - 4 (x + 1) y^{'} = 0$	[_linear]	✓

7917	$x y^{'} + y = x$	[_linear]	✓

7918	$x^{2} y^{'} + y = x^{2}$	[_linear]	✓

7919	$x^{2} y^{'} = y$	[_separable]	✓

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

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

7926	$x^{2} y^{'} - 2 y = 3 x^{2}$ i.c.	[_linear]	✓

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

8069	$y^{'} + y = \cos (x)$	[[_linear, ‘class A‘]]	✓

8073	$y^{'} = 2 x y$	[_separable]	✓

8083	$y^{'} - y = x^{2}$	[[_linear, ‘class A‘]]	✓

8085	$x y^{'} = y$	[_separable]	✓

8087	$x^{2} y^{'} = y$	[_separable]	✓

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

8090	$y^{'} + \frac{y}{x} = x$	[_linear]	✓

8094	$y^{'} = x - y$ i.c.	[[_linear, ‘class A‘]]	✓

8215	$y^{'} - 2 y = x^{2}$ i.c.	[[_linear, ‘class A‘]]	✓

8436	$x {y^{'}}^{2} - (2 x + 3 y) y^{'} + 6 y = 0$	[_quadrature]	✓

8438	$x^{2} {y^{'}}^{2} + x y^{'} - y^{2} - y = 0$	[_separable]	✓

8439	$x {y^{'}}^{2} + (1 - x^{2} y) y^{'} - x y = 0$	[_quadrature]	✓

8440	${y^{'}}^{2} - (x^{2} y + 3) y^{'} + 3 x^{2} y = 0$	[_quadrature]	✓

8442	${y^{'}}^{2} - y^{2} x^{2} = 0$	[_separable]	✓

8445	${y^{'}}^{2} - x y (x + y) y^{'} + x^{3} y^{3} = 0$	[_separable]	✓

8452	$x {y^{'}}^{3} - (x + x^{2} + y) {y^{'}}^{2} + (x^{2} + y + x y) y^{'} - x y = 0$	[_quadrature]	✓

8534	$6 x {y^{'}}^{2} - (3 x + 2 y) y^{'} + y = 0$	[_quadrature]	✓

8553	$x {y^{'}}^{2} + (1 - x) y y^{'} - y^{2} = 0$	[_quadrature]	✓

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

8699	$y^{'} + \frac{2 y}{x} = 5 x^{2}$	[_linear]	✓

8700	$t x^{'} + 2 x = 4 e^{t}$	[_linear]	✓

8723	$y^{'} = x + \frac{\sec (x) y}{x}$	[_linear]	✓

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

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

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

8990	$y^{'} = y a x$	[_separable]	✓

8991	$y^{'} = a x + y$	[[_linear, ‘class A‘]]	✓

8992	$y^{'} = a x + b y$	[[_linear, ‘class A‘]]	✓

8999	$c y^{'} = a x + y$	[[_linear, ‘class A‘]]	✓

9000	$c y^{'} = a x + b y$	[[_linear, ‘class A‘]]	✓

9010	$y^{'} = \sin (x) + y$	[[_linear, ‘class A‘]]	✓

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

9036	${y^{'}}^{2} = \frac{y^{2}}{x}$	[_separable]	✓

9162	$y^{'} + y \cot (x) = 2 \cos (x)$	[_linear]	✓

10016	$y^{'} + a y - c e^{b x} = 0$	[[_linear, ‘class A‘]]	✓

10017	$y^{'} + a y - b \sin (c x) = 0$	[[_linear, ‘class A‘]]	✓

10018	$y^{'} + 2 x y - x e^{- x^{2}} = 0$	[_linear]	✓

10019	$y^{'} + y \cos (x) - e^{2 x} = 0$	[_linear]	✓

10020	$y^{'} + y \cos (x) - \frac{\sin (2 x)}{2} = 0$	[_linear]	✓

10021	$y^{'} + y \cos (x) - e^{- \sin (x)} = 0$	[_linear]	✓

10022	$y^{'} + y \tan (x) - \sin (2 x) = 0$	[_linear]	✓

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

10024	$y^{'} + f^{'} (x) y - f (x) f^{'} (x) = 0$	[_linear]	✓

10025	$y^{'} + f (x) y - g (x) = 0$	[_linear]	✓

10102	$x y^{'} + y - x \sin (x) = 0$	[_linear]	✓

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]	✓

10106	$x y^{'} + a y + b x^{n} = 0$	[_linear]	✓

10141	$2 x y^{'} - y - 2 x^{3} = 0$	[_linear]	✓

10144	$x^{2} y^{'} + y - x = 0$	[_linear]	✓

10145	$x^{2} y^{'} - y + x^{2} e^{x - \frac{1}{x}} = 0$	[_linear]	✓

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

10159	$(x^{2} + 1) y^{'} + x y - 1 = 0$	[_linear]	✓

10160	$(x^{2} + 1) y^{'} + x y - x (x^{2} + 1) = 0$	[_linear]	✓

10161	$(x^{2} + 1) y^{'} + 2 x y - 2 x^{2} = 0$	[_linear]	✓

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

10165	$(x^{2} - 1) y^{'} + 2 x y - \cos (x) = 0$	[_linear]	✓

10172	$(x^{2} - 5 x + 6) y^{'} + 3 x y - 8 y + x^{2} = 0$	[_linear]	✓

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]	✓

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

10203	$\sqrt{a^{2} + x^{2}} y^{'} + y - \sqrt{a^{2} + x^{2}} + x = 0$	[_linear]	✓

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

10207	$\cos (x) y^{'} + y + (\sin (x) + 1) \cos (x) = 0$	[_linear]	✓

10209	$\sin (x) \cos (x) y^{'} - y - \sin {(x)}^{3} = 0$	[_linear]	✓

10211	$(a \sin {(x)}^{2} + b) y^{'} + a y \sin (2 x) + A x (a \sin {(x)}^{2} + c) = 0$	[_linear]	✓

10398	${y^{'}}^{2} + 2 y y^{'} \cot (x) - y^{2} = 0$	[_separable]	✓

10399	${y^{'}}^{2} + y (y - x) y^{'} - x y^{3} = 0$	[_separable]	✓

10442	$x^{2} {y^{'}}^{2} + 3 x y y^{'} + 3 y^{2} = 0$	[_separable]	✓

10445	$x^{2} {y^{'}}^{2} + (x^{2} y - 2 x y + x^{3}) y^{'} + (y^{2} - x^{2} y) (1 - x) = 0$	[_linear]	✓

10451	$(- a^{2} + x^{2}) {y^{'}}^{2} + 2 x y y^{'} + y^{2} = 0$	[_separable]	✓

10526	${y^{'}}^{2} - a x y y^{'} + 2 a y^{2} = 0$	[_separable]	✓

10527	${y^{'}}^{3} - (y^{2} + x y + x^{2}) {y^{'}}^{2} + (x^{3} y + y^{2} x^{2} + x y^{3}) y^{'} - x^{3} y^{3} = 0$	[_quadrature]	✓

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

11925	$g (x) y^{'} = f_{1} (x) y + f_{0} (x)$	[_linear]	✓

12086	$y^{'} = a \ln {(x)}^{n} y - a b x \ln {(x)}^{n + 1} y + b \ln (x) + b$	[_linear]	✓

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

12740	$y^{'} + y \cot (x) = \sec (x)$	[_linear]	✓

12741	$x y^{'} + (x + 1) y = e^{x}$	[_linear]	✓

12742	$y^{'} - \frac{2 y}{x + 1} = {(x + 1)}^{3}$	[_linear]	✓

12743	$(x^{3} + x) y^{'} + 4 x^{2} y = 2$	[_linear]	✓

12744	$x^{2} y^{'} + (1 - 2 x) y = x^{2}$	[_linear]	✓

12751	$y^{2} (3 y - 6 x y^{'}) - x (y - 2 x y^{'}) = 0$	[_separable]	✓

12762	$x^{3} y - y^{4} + (x y^{3} - x^{4}) y^{'} = 0$	[_separable]	✓

12764	$x y^{'} - y + 2 x^{2} y - x^{3} = 0$	[_linear]	✓

12770	$y^{'} - x^{2} y = x^{5}$	[_linear]	✓

12779	$y^{'} + \frac{y}{{(- x^{2} + 1)}^{3 / 2}} = \frac{x + \sqrt{- x^{2} + 1}}{{(- x^{2} + 1)}^{2}}$	[_linear]	✓

12782	$(x^{2} + 1) y^{'} + y = \arctan (x)$	[_linear]	✓

12784	$y^{'} + y \cos (x) = \frac{\sin (2 x)}{2}$	[_linear]	✓

12800	${(2 x y^{'} - y)}^{2} = 8 x^{3}$	[_linear]	✓

12802	${y^{'}}^{3} - (2 x + y^{2}) {y^{'}}^{2} + (x^{2} - y^{2} + 2 x y^{2}) y^{'} - (x^{2} - y^{2}) y^{2} = 0$	[_quadrature]	✓

12828	${y^{'}}^{2} + 2 y y^{'} \cot (x) = y^{2}$	[_separable]	✓

12830	$x^{2} {y^{'}}^{2} - 2 (x y + 2 y^{'}) y^{'} + y^{2} = 0$	[_separable]	✓

12946	$x^{'} = \frac{2 x}{t}$	[_separable]	✓

12951	$x^{'} + 2 x = t^{2} + 4 t + 7$	[[_linear, ‘class A‘]]	✓

12952	$2 t x^{'} = x$	[_separable]	✓

12973	$x^{'} = \frac{2 x}{t + 1}$	[_separable]	✓

12992	$x^{'} e^{2 t} + 2 x e^{2 t} = e^{- t}$ i.c.	[[_linear, ‘class A‘]]	✓

12996	$x^{'} = 2 t^{3} x - 6$	[_linear]	✓

12999	$7 t^{2} x^{'} = 3 x - 2 t$	[_linear]	✓

13002	$x^{'} = - \frac{2 x}{t} + t$	[_linear]	✓

13003	$y^{'} + y = e^{t}$	[[_linear, ‘class A‘]]	✓

13004	$x^{'} + 2 t x = e^{- t^{2}}$	[_linear]	✓

13005	$t x^{'} = - x + t^{2}$	[_linear]	✓

13006	$θ^{'} = - a θ + e^{t b}$	[[_linear, ‘class A‘]]	✓

13007	$(t^{2} + 1) x^{'} = - 3 t x + 6 t$	[_separable]	✓

13008	$x^{'} + \frac{5 x}{t} = t + 1$ i.c.	[_linear]	✓

13009	$x^{'} = (a + \frac{b}{t}) x$ i.c.	[_separable]	✓

13010	$R^{'} + \frac{R}{t} = \frac{2}{t^{2} + 1}$ i.c.	[_linear]	✓

13011	$N^{'} = N - 9 e^{- t}$	[[_linear, ‘class A‘]]	✓

13012	$\cos (θ) v^{'} + v = 3$	[_separable]	✓

13013	$R^{'} = \frac{R}{t} + t e^{- t}$ i.c.	[_linear]	✓

13014	$y^{'} + a y = \sqrt{t + 1}$	[[_linear, ‘class A‘]]	✓

13015	$x^{'} = 2 t x$	[_separable]	✓

13016	$x^{'} + \frac{e^{- t} x}{t} = t$ i.c.	[_linear]	✓

13020	$x^{'} + p (t) x = 0$	[_separable]	✓

13027	$x^{3} + 3 t x^{2} x^{'} = 0$	[_separable]	✓

13167	$y^{'} + y = x + 1$	[[_linear, ‘class A‘]]	✓

13173	$y^{'} + 3 y = 3 x^{2} e^{- 3 x}$	[[_linear, ‘class A‘]]	✓

13174	$y^{'} + 4 x y = 8 x$	[_separable]	✓

13179	$2 y + y^{'} = 6 e^{x} + 4 x e^{- 2 x}$	[[_linear, ‘class A‘]]	✓

13183	$y^{'} + y = 2 x e^{- x}$ i.c.	[[_linear, ‘class A‘]]	✓

13184	$y^{'} + y = 2 x e^{- x}$ i.c.	[[_linear, ‘class A‘]]	✓

13211	$4 x y + (x^{2} + 1) y^{'} = 0$	[_separable]	✓

13212	$x y + 2 x + y + 2 + (x^{2} + 2 x) y^{'} = 0$	[_separable]	✓

13218	$x + y - x y^{'} = 0$	[_linear]	✓

13235	$y^{'} + \frac{3 y}{x} = 6 x^{2}$	[_linear]	✓

13236	$x^{4} y^{'} + 2 x^{3} y = 1$	[_linear]	✓

13237	$y^{'} + 3 y = 3 x^{2} e^{- 3 x}$	[[_linear, ‘class A‘]]	✓

13238	$y^{'} + 4 x y = 8 x$	[_separable]	✓

13239	$x^{'} + \frac{x}{t^{2}} = \frac{1}{t^{2}}$	[_separable]	✓

13240	$(u^{2} + 1) v^{'} + 4 u v = 3 u$	[_separable]	✓

13241	$x y^{'} + \frac{(2 x + 1) y}{x + 1} = - 1 + x$	[_linear]	✓

13242	$(x^{2} + x - 2) y^{'} + 3 (x + 1) y = - 1 + x$	[_linear]	✓

13243	$x y^{'} + x y + y - 1 = 0$	[_linear]	✓

13245	$r^{'} + r \tan (t) = \cos (t)$	[_linear]	✓

13246	$\cos (t) r^{'} + r \sin (t) - \cos {(t)}^{4} = 0$	[_linear]	✓

13247	$\cos {(x)}^{2} - y \cos (x) - (\sin (x) + 1) y^{'} = 0$	[_linear]	✓

13248	$y \sin (2 x) - \cos (x) + (1 + \sin {(x)}^{2}) y^{'} = 0$	[_linear]	✓

13253	$x y^{'} - 2 y = 2 x^{4}$ i.c.	[_linear]	✓

13254	$y^{'} + 3 x^{2} y = x^{2}$ i.c.	[_separable]	✓

13255	$e^{x} (y - 3 {(e^{x} + 1)}^{2}) + (e^{x} + 1) y^{'} = 0$ i.c.	[_linear]	✓

13256	$2 x (y + 1) - (x^{2} + 1) y^{'} = 0$ i.c.	[_separable]	✓

13257	$r^{'} + r \tan (t) = \cos {(t)}^{2}$ i.c.	[_linear]	✓

13258	$x^{'} - x = \sin (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓

13261	$y^{'} + y = {\begin{array}{cc} 2 & 0 \leq x < 1 \\ 0 & 1 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

13262	$y^{'} + y = {\begin{array}{cc} 5 & 0 \leq x < 10 \\ 1 & 10 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

13263	$y^{'} + y = {\begin{array}{cc} e^{- x} & 0 \leq x < 2 \\ e^{- 2} & 2 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

13264	$(x + 2) y^{'} + y = {\begin{array}{cc} 2 x & 0 \leq x < 2 \\ 4 & 2 \leq x \end{array}$ i.c.	[_linear]	✓

13265	$a y^{'} + b y = k e^{- λ x}$	[[_linear, ‘class A‘]]	✓

13266	$y^{'} + y = 2 \sin (x) + 5 \sin (2 x)$	[[_linear, ‘class A‘]]	✓

13272	$6 x^{2} y - (x^{3} + 1) y^{'} = 0$	[_separable]	✓

13274	$y - 1 + x (x + 1) y^{'} = 0$	[_separable]	✓

13275	$x^{2} - 2 y + x y^{'} = 0$	[_linear]	✓

13277	$e^{2 x} y^{2} + (e^{2 x} y - 2 y) y^{'} = 0$	[_separable]	✓

13278	$8 x^{3} y - 12 x^{3} + (x^{4} + 1) y^{'} = 0$	[_separable]	✓

13281	$(x + 1) y^{'} + x y = e^{- x}$	[_linear]	✓

13284	$(x^{3} + 1) y^{'} + 6 x^{2} y = 6 x^{2}$	[_separable]	✓

13292	$y^{'} = \frac{x y}{x^{2} + 1}$ i.c.	[_separable]	✓

13293	$y^{'} + y = {\begin{array}{cc} 1 & 0 \leq x < 2 \\ 0 & 0 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

13294	$(x + 2) y^{'} + y = {\begin{array}{cc} 2 x & 0 \leq x \leq 2 \\ 4 & 2 < x \end{array}$ i.c.	[_linear]	✓

13634	$x^{'} e^{3 t} + 3 x e^{3 t} = e^{- t}$ i.c.	[[_linear, ‘class A‘]]	✓

13640	$x^{'} = t^{3} (- x + 1)$ i.c.	[_separable]	✓

13642	$x^{'} = x t^{2}$	[_separable]	✓

13646	$x y^{'} = k y$	[_separable]	✓

13647	$i^{'} = p (t) i$	[_separable]	✓

13652	$y^{'} + \frac{y}{x} = x^{2}$	[_linear]	✓

13653	$x^{'} + t x = 4 t$ i.c.	[_separable]	✓

13654	$z^{'} = z \tan (y) + \sin (y)$	[_linear]	✓

13655	$y^{'} + e^{- x} y = 1$ i.c.	[_linear]	✓

13656	$x^{'} + x \tanh (t) = 3$	[_linear]	✓

13657	$y^{'} + 2 y \cot (x) = 5$ i.c.	[_linear]	✓

13658	$x^{'} + 5 x = t$	[[_linear, ‘class A‘]]	✓

13659	$x^{'} + (a + \frac{1}{t}) x = b$ i.c.	[_linear]	✓

13660	$T^{'} = - k (T - μ - a \cos (ω (t - ϕ)))$	[[_linear, ‘class A‘]]	✓

13662	$1 + y e^{x} + x e^{x} y + (x e^{x} + 2) y^{'} = 0$	[_linear]	✓

13772	$x y^{'} + y = x^{3}$	[_linear]	✓

13774	$x^{'} + 3 x = e^{2 t}$	[[_linear, ‘class A‘]]	✓

13775	$\cos (x) y^{'} + y \sin (x) = 1$	[_linear]	✓

13777	$x^{'} = x + \sin (t)$	[[_linear, ‘class A‘]]	✓

13799	$x^{'} + 5 x = 10 t + 2$ i.c.	[[_linear, ‘class A‘]]	✓

13804	$x^{'} - x \cot (t) = 4 \sin (t)$	[_linear]	✓

13813	$(x^{2} - 1) y^{'} + 2 x y - \cos (x) = 0$	[_linear]	✓

13820	${y^{'}}^{2} + 2 y y^{'} \cot (x) - y^{2} = 0$	[_separable]	✓

13885	$\cos (x) y^{'} + y e^{x^{2}} = \sinh (x)$	[_linear]	✓

13889	$5 y^{'} - x y = 0$	[_separable]	✓

14075	$y^{'} + y \cos (x) = \frac{\sin (2 x)}{2}$	[_linear]	✓

14083	$y - x y^{'} = 0$	[_separable]	✓

14085	$1 + y - (1 - x) y^{'} = 0$	[_separable]	✓

14087	$y - a + x^{2} y^{'} = 0$	[_separable]	✓

14088	$z - (- a^{2} + t^{2}) z^{'} = 0$	[_separable]	✓

14091	$r^{'} + r \tan (t) = 0$	[_separable]	✓

14097	$y + x + x y^{'} = 0$	[_linear]	✓

14102	$t - s + t s^{'} = 0$	[_linear]	✓

14107	$x + 2 y + 1 - (2 x - 3) y^{'} = 0$	[_linear]	✓

14112	$y^{'} - \frac{2 y}{x + 1} = {(x + 1)}^{3}$	[_linear]	✓

14113	$y^{'} - \frac{a y}{x} = \frac{x + 1}{x}$	[_linear]	✓

14114	$(- x^{2} + x) y^{'} + (2 x^{2} - 1) y - a x^{3} = 0$	[_linear]	✓

14115	$s^{'} \cos (t) + s \sin (t) = 1$	[_linear]	✓

14116	$s^{'} + s \cos (t) = \frac{\sin (2 t)}{2}$	[_linear]	✓

14117	$y^{'} - \frac{n y}{x} = e^{x} x^{n}$	[_linear]	✓

14118	$y^{'} + \frac{n y}{x} = a x^{- n}$	[_linear]	✓

14119	$y^{'} + y = e^{- x}$	[[_linear, ‘class A‘]]	✓

14120	$y^{'} + \frac{(1 - 2 x) y}{x^{2}} - 1 = 0$	[_linear]	✓

14142	$y = x y^{'} + y^{'}$	[_separable]	✓

14145	$y^{'} = \frac{2 y}{x} - \sqrt{3}$	[_linear]	✓

14200	$(x^{2} + 1) y^{'} - x y - α = 0$	[_linear]	✓

14210	$y^{'} + \frac{y}{x} = e^{x}$ i.c.	[_linear]	✓

14232	$- y + x y^{'} = 0$	[_separable]	✓

14237	$y^{'} - \frac{y}{x} = 1$	[_linear]	✓

14239	$2 x y + x^{2} y^{'} = 0$	[_separable]	✓

14247	$2 x y^{'} - y = 0$	[_separable]	✓

14254	$y^{'} - 2 x y = 0$	[_separable]	✓

14255	$y^{'} + y = x^{2} + 2 x - 1$	[[_linear, ‘class A‘]]	✓

14260	$x \ln (x) y^{'} - (1 + \ln (x)) y = 0$	[_separable]	✓

14278	$y^{'} = x y$	[_separable]	✓

14279	$y^{'} = - x y$	[_separable]	✓

14282	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓

14283	$y^{'} = x y$	[_separable]	✓

14285	$y^{'} = \frac{y}{x}$	[_separable]	✓

14294	$y^{'} = \frac{3 y}{(x - 5) (x + 3)} + e^{- x}$	[_linear]	✓

14310	$y^{'} = x y + \frac{1}{x^{2} + 1}$ i.c.	[_linear]	✓

14311	$y^{'} = \cos (x) + \frac{y}{x}$ i.c.	[_linear]	✓

14312	$y^{'} = \frac{y}{x} + \tan (x)$ i.c.	[_linear]	✓

14313	$y^{'} = \frac{y}{- x^{2} + 4} + \sqrt{x}$ i.c.	[_linear]	✓

14314	$y^{'} = \frac{y}{- x^{2} + 4} + \sqrt{x}$ i.c.	[_linear]	✓

14315	$y^{'} = y \cot (x) + \csc (x)$ i.c.	[_linear]	✓

14332	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

14335	$y^{'} = x y + x$ i.c.	[_separable]	✓

14337	$y - x^{2} y^{'} = 0$ i.c.	[_separable]	✓

14340	$y^{'} = \frac{1 - x y}{x^{2}}$	[_linear]	✓

14344	$y^{'} = x y + 2$ i.c.	[_linear]	✓

14345	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

14346	$y^{'} = \frac{y}{- 1 + x} + x^{2}$ i.c.	[_linear]	✓

14347	$y^{'} = \frac{y}{x} + \sin (x^{2})$ i.c.	[_linear]	✓

14348	$y^{'} = \frac{2 y}{x} + e^{x}$ i.c.	[_linear]	✓

14349	$y^{'} = y \cot (x) + \sin (x)$ i.c.	[_linear]	✓

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]	✓

14357	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓

14358	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

14359	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

14360	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$ i.c.	[_linear]	✓

14361	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$	[_linear]	✓

14362	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$ i.c.	[_linear]	✓

14522	$y^{'} = \frac{y + 1}{t + 1}$	[_separable]	✓

14524	$y^{'} = t^{4} y$	[_separable]	✓

14534	$y^{'} = \frac{2 y + 1}{t}$	[_separable]	✓

14537	$v^{'} = t^{2} v - 2 - 2 v + t^{2}$	[_separable]	✓

14541	$w^{'} = \frac{w}{t}$	[_separable]	✓

14543	$x^{'} = - t x$ i.c.	[_separable]	✓

14544	$y^{'} = t y$ i.c.	[_separable]	✓

14562	$y^{'} = y + t + 1$	[[_linear, ‘class A‘]]	✓

14564	$y^{'} = 2 y - t$ i.c.	[[_linear, ‘class A‘]]	✓

14566	$y^{'} = (t + 1) y$ i.c.	[_separable]	✓

14577	$y^{'} = t^{2} + t^{2} y$	[_separable]	✓

14578	$y^{'} = t + t y$	[_separable]	✓

14585	$v^{'} = 2 V (t) - 2 v$	[[_linear, ‘class A‘]]	✓

14647	$y^{'} = - 4 y + 9 e^{- t}$	[[_linear, ‘class A‘]]	✓

14648	$y^{'} = - 4 y + 3 e^{- t}$	[[_linear, ‘class A‘]]	✓

14649	$y^{'} = - 3 y + 4 \cos (2 t)$	[[_linear, ‘class A‘]]	✓

14650	$y^{'} = 2 y + \sin (2 t)$	[[_linear, ‘class A‘]]	✓

14651	$y^{'} = 3 y - 4 e^{3 t}$	[[_linear, ‘class A‘]]	✓

14652	$y^{'} = \frac{y}{2} + 4 e^{\frac{t}{2}}$	[[_linear, ‘class A‘]]	✓

14653	$y^{'} + 2 y = e^{\frac{t}{3}}$ i.c.	[[_linear, ‘class A‘]]	✓

14654	$y^{'} - 2 y = 3 e^{- 2 t}$ i.c.	[[_linear, ‘class A‘]]	✓

14655	$y^{'} + y = \cos (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓

14656	$y^{'} + 3 y = \cos (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓

14657	$y^{'} - 2 y = 7 e^{2 t}$ i.c.	[[_linear, ‘class A‘]]	✓

14658	$y^{'} + 2 y = 3 t^{2} + 2 t - 1$	[[_linear, ‘class A‘]]	✓

14659	$y^{'} + 2 y = t^{2} + 2 t + 1 + e^{4 t}$	[[_linear, ‘class A‘]]	✓

14660	$y^{'} + y = t^{3} + \sin (3 t)$	[[_linear, ‘class A‘]]	✓

14661	$y^{'} - 3 y = 2 t - e^{4 t}$	[[_linear, ‘class A‘]]	✓

14662	$y^{'} + y = \cos (2 t) + 3 \sin (2 t) + e^{- t}$	[[_linear, ‘class A‘]]	✓

14663	$y^{'} = - \frac{y}{t} + 2$	[_linear]	✓

14664	$y^{'} = \frac{3 y}{t} + t^{5}$	[_linear]	✓

14665	$y^{'} = - \frac{y}{t + 1} + t^{2}$	[_linear]	✓

14666	$y^{'} = - 2 t y + 4 e^{- t^{2}}$	[_linear]	✓

14667	$y^{'} - \frac{2 t y}{t^{2} + 1} = 3$	[_linear]	✓

14668	$y^{'} - \frac{2 y}{t} = t^{3} e^{t}$	[_linear]	✓

14669	$y^{'} = - \frac{y}{t + 1} + 2$ i.c.	[_linear]	✓

14670	$y^{'} = \frac{y}{t + 1} + 4 t^{2} + 4 t$ i.c.	[_linear]	✓

14671	$y^{'} = - \frac{y}{t} + 2$ i.c.	[_linear]	✓

14672	$y^{'} = - 2 t y + 4 e^{- t^{2}}$ i.c.	[_linear]	✓

14673	$y^{'} - \frac{2 y}{t} = 2 t^{2}$ i.c.	[_linear]	✓

14674	$y^{'} - \frac{3 y}{t} = 2 t^{3} e^{2 t}$ i.c.	[_linear]	✓

14675	$y^{'} = \sin (t) y + 4$	[_linear]	✓

14676	$y^{'} = t^{2} y + 4$	[_linear]	✓

14677	$y^{'} = \frac{y}{t^{2}} + 4 \cos (t)$	[_linear]	✓

14678	$y^{'} = y + 4 \cos (t^{2})$	[[_linear, ‘class A‘]]	✓

14679	$y^{'} = - y e^{- t^{2}} + \cos (t)$	[_linear]	✓

14680	$y^{'} = \frac{y}{\sqrt{t^{3} - 3}} + t$	[_linear]	✓

14681	$y^{'} = a t y + 4 e^{- t^{2}}$	[_linear]	✓

14682	$y^{'} = t^{r} y + 4$	[_linear]	✓

14683	$v^{'} + \frac{2 v}{5} = 3 \cos (2 t)$	[[_linear, ‘class A‘]]	✓

14684	$y^{'} = - 2 t y + 4 e^{- t^{2}}$	[_linear]	✓

14685	$y^{'} + 2 y = 3 e^{- 2 t}$	[[_linear, ‘class A‘]]	✓

14692	$y^{'} = y + e^{- t}$	[[_linear, ‘class A‘]]	✓

14694	$y^{'} = t y$	[_separable]	✓

14695	$y^{'} = 3 y + e^{7 t}$	[[_linear, ‘class A‘]]	✓

14696	$y^{'} = \frac{t y}{t^{2} + 1}$	[_separable]	✓

14697	$y^{'} = - 5 y + \sin (3 t)$	[[_linear, ‘class A‘]]	✓

14698	$y^{'} = t + \frac{2 y}{t + 1}$	[_linear]	✓

14701	$y^{'} = - 3 y + e^{- 2 t} + t^{2}$	[[_linear, ‘class A‘]]	✓

14702	$x^{'} = - t x$ i.c.	[_separable]	✓

14703	$y^{'} = 2 y + \cos (4 t)$ i.c.	[[_linear, ‘class A‘]]	✓

14704	$y^{'} = 3 y + 2 e^{3 t}$ i.c.	[[_linear, ‘class A‘]]	✓

14706	$y^{'} + 5 y = 3 e^{- 5 t}$ i.c.	[[_linear, ‘class A‘]]	✓

14707	$y^{'} = 2 t y + 3 t e^{t^{2}}$ i.c.	[_linear]	✓

14715	$y^{'} = t^{2} y + 1 + y + t^{2}$	[_separable]	✓

14716	$y^{'} = \frac{2 y + 1}{t}$	[_separable]	✓

14902	$y^{'} + 4 y = e^{2 x}$	[[_linear, ‘class A‘]]	✓

14945	$y^{'} + 3 x y = 6 x$	[_separable]	✓

14951	$(- 2 + x) y^{'} = 3 + y$	[_separable]	✓

14957	$y^{'} = 3 x - y \sin (x)$	[_linear]	✓

14961	$y^{'} + x y = 4 x$	[_separable]	✓

14962	$y^{'} + 4 y = x^{2}$	[[_linear, ‘class A‘]]	✓

14963	$y^{'} = x y - 3 x - 2 y + 6$	[_separable]	✓

14973	$y^{'} = 2 x - 1 + 2 x y - y$ i.c.	[_separable]	✓

14976	$y^{'} = x y - 4 x$	[_separable]	✓

14982	$y^{'} = x y - 4 x$	[_separable]	✓

14983	$y^{'} = x y - 3 x - 2 y + 6$	[_separable]	✓

14986	$y^{'} = \frac{y}{x}$	[_separable]	✓

14999	$y^{'} = 2 x - 1 + 2 x y - y$ i.c.	[_separable]	✓

15004	$x^{2} y^{'} + 3 x^{2} y = \sin (x)$	[[_linear, ‘class A‘]]	✓

15008	$y^{'} = 1 + x y + 3 y$	[_linear]	✓

15011	$y^{'} = y \sin (x)$	[_separable]	✓

15013	$x y^{'} + \cos (x^{2}) = 827 y$	[_linear]	✓

15015	$2 y + y^{'} = 20 e^{3 x}$	[[_linear, ‘class A‘]]	✓

15016	$y^{'} = 4 y + 16 x$	[[_linear, ‘class A‘]]	✓

15017	$y^{'} - 2 x y = x$	[_separable]	✓

15018	$x y^{'} + 3 y - 10 x^{2} = 0$	[_linear]	✓

15019	$2 x y + x^{2} y^{'} = \sin (x)$	[_linear]	✓

15020	$x y^{'} = \sqrt{x} + 3 y$	[_linear]	✓

15021	$\cos (x) y^{'} + y \sin (x) = \cos {(x)}^{2}$	[_linear]	✓

15022	$x y^{'} + (5 x + 2) y = \frac{20}{x}$	[_linear]	✓

15023	$2 \sqrt{x} y^{'} + y = 2 x e^{- \sqrt{x}}$	[_linear]	✓

15026	$y^{'} + 5 y = e^{- 3 x}$ i.c.	[[_linear, ‘class A‘]]	✓

15027	$x y^{'} + 3 y = 20 x^{2}$ i.c.	[_linear]	✓

15028	$x y^{'} = y + x^{2} \cos (x)$ i.c.	[_linear]	✓

15029	$(x^{2} + 1) y^{'} = x (3 + 3 x^{2} - y)$ i.c.	[_linear]	✓

15030	$y^{'} + 6 x y = \sin (x)$ i.c.	[_linear]	✓

15031	$x^{2} y^{'} + x y = \sqrt{x} \sin (x)$ i.c.	[_linear]	✓

15032	$- y + x y^{'} = x^{2} e^{- x^{2}}$ i.c.	[_linear]	✓

15076	$2 x (y + 1) - y^{'} = 0$	[_separable]	✓

15080	$x y^{'} = 2 y - 6 x^{3}$	[_linear]	✓

15087	$4 x y - 6 + x^{2} y^{'} = 0$	[_linear]	✓

15090	$3 y - x^{3} + x y^{'} = 0$	[_linear]	✓

15093	$2 + 2 x^{2} - 2 x y + (x^{2} + 1) y^{'} = 0$	[_linear]	✓

15109	$y^{'} - 3 y = 12 e^{2 x}$	[[_linear, ‘class A‘]]	✓

15114	$2 y - 6 x + (x + 1) y^{'} = 0$	[_linear]	✓

15120	$2 y + y^{'} = \sin (x)$	[[_linear, ‘class A‘]]	✓

15127	$y^{'} = x (6 y + e^{x^{2}})$	[_linear]	✓

15129	$x^{2} y^{'} + 3 x y = 6 e^{- x^{2}}$	[_linear]	✓

15187	$x y^{'} + 3 y = e^{2 x}$	[_linear]	✓

15712	$y^{'} + x y = 0$	[_separable]	✓

15713	$y^{'} + y = \sin (x)$	[[_linear, ‘class A‘]]	✓

15725	$y^{'} = - \frac{2 y}{x} - 3$	[_linear]	✓

15742	$y^{'} + y = \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓

15755	$x y^{'} + y = \cos (x)$	[_linear]	✓

15763	$y^{'} + y \cos (x) = 0$	[_separable]	✓

15764	$y^{'} - y = \sin (x)$	[[_linear, ‘class A‘]]	✓

15777	$2 y + y^{'} = x^{2}$ i.c.	[[_linear, ‘class A‘]]	✓

15784	$y^{'} = y + \frac{1}{- t + 1}$	[_linear]	✓

15788	$y^{'} = y \sqrt{t}$ i.c.	[_separable]	✓

15790	$t y^{'} = y$	[_separable]	✓

15791	$y^{'} = y \tan (t)$ i.c.	[_separable]	✓

15801	$t y^{'} + y = t^{3}$ i.c.	[_linear]	✓

15802	$t^{3} y^{'} + t^{4} y = 2 t^{3}$ i.c.	[_linear]	✓

15803	$2 y^{'} + t y = \ln (t)$ i.c.	[_linear]	✓

15804	$y^{'} + y \sec (t) = t$ i.c.	[_linear]	✓

15805	$y^{'} + \frac{y}{t - 3} = \frac{1}{t - 1}$ i.c.	[_linear]	✓

15806	$(t - 2) y^{'} + (t^{2} - 4) y = \frac{1}{t + 2}$ i.c.	[_linear]	✓

15807	$y^{'} + \frac{y}{\sqrt{- t^{2} + 4}} = t$ i.c.	[_linear]	✓

15808	$y^{'} + \frac{y}{\sqrt{- t^{2} + 4}} = t$ i.c.	[_linear]	✓

15809	$t y^{'} + y = t \sin (t)$ i.c.	[_linear]	✓

15810	$y^{'} + y \tan (t) = \sin (t)$ i.c.	[_linear]	✓

15822	$y^{'} = \frac{y + 1}{t + 1}$	[_separable]	✓

15823	$y^{'} = \frac{2 + y}{2 t + 1}$	[_separable]	✓

15867	$y^{'} = \frac{3 + y}{3 x + 1}$ i.c.	[_separable]	✓

15870	$y^{'} = \frac{3 y + 1}{x + 3}$ i.c.	[_separable]	✓

15871	$y^{'} = y \cos (t)$ i.c.	[_separable]	✓

15874	$y^{'} + y f (t) = 0$ i.c.	[_separable]	✓

15875	$y^{'} = - \frac{y - 2}{- 2 + x}$ i.c.	[_separable]	✓

15885	$y^{'} = y f (t)$ i.c.	[_separable]	✓

15887	$y^{'} - y = 2 e^{- t}$	[[_linear, ‘class A‘]]	✓

15888	$y^{'} - y = 2 \cos (t)$	[[_linear, ‘class A‘]]	✓

15889	$y^{'} - y = t^{2} - 2 t$	[[_linear, ‘class A‘]]	✓

15890	$y^{'} - y = 4 t e^{- t}$	[[_linear, ‘class A‘]]	✓

15891	$t y^{'} + y = t^{2}$	[_linear]	✓

15892	$t y^{'} + y = t$	[_linear]	✓

15893	$x y^{'} + y = x e^{x}$	[_linear]	✓

15894	$x y^{'} + y = e^{- x}$	[_linear]	✓

15895	$y^{'} - \frac{2 t y}{t^{2} + 1} = 2$	[_linear]	✓

15896	$y^{'} - \frac{4 t y}{4 t^{2} + 1} = 4 t$	[_linear]	✓

15897	$y^{'} = 2 x + \frac{x y}{x^{2} - 1}$	[_linear]	✓

15898	$y^{'} + y \cot (t) = \cos (t)$	[_linear]	✓

15899	$y^{'} - \frac{3 t y}{t^{2} - 4} = t$	[_linear]	✓

15900	$y^{'} - \frac{4 t y}{4 t^{2} - 9} = t$	[_linear]	✓

15901	$y^{'} - \frac{9 x y}{9 x^{2} + 49} = x$	[_linear]	✓

15902	$y^{'} + 2 y \cot (x) = \cos (x)$	[_linear]	✓

15903	$y^{'} + x y = x^{3}$	[_linear]	✓

15904	$y^{'} - x y = x$	[_separable]	✓

15906	$y^{'} - x = y$	[[_linear, ‘class A‘]]	✓

15908	$x^{'} = \frac{3 x t^{2}}{- t^{3} + 1}$	[_separable]	✓

15909	$p^{'} = t^{3} + \frac{p}{t}$	[_linear]	✓

15910	$v^{'} + v = e^{- s}$	[[_linear, ‘class A‘]]	✓

15911	$y^{'} - y = 4 e^{t}$ i.c.	[[_linear, ‘class A‘]]	✓

15912	$y^{'} + y = e^{- t}$ i.c.	[[_linear, ‘class A‘]]	✓

15913	$y^{'} + 3 t^{2} y = e^{- t^{3}}$ i.c.	[_linear]	✓

15914	$y^{'} + 2 t y = 2 t$ i.c.	[_separable]	✓

15915	$t y^{'} + y = \cos (t)$ i.c.	[_linear]	✓

15916	$t y^{'} + y = 2 t e^{t}$ i.c.	[_linear]	✓

15917	$(1 + e^{t}) y^{'} + e^{t} y = t$ i.c.	[_linear]	✓

15918	$(t^{2} + 4) y^{'} + 2 t y = 2 t$ i.c.	[_separable]	✓

15919	$x^{'} = x + t + 1$ i.c.	[[_linear, ‘class A‘]]	✓

15920	$y^{'} = e^{2 t} + 2 y$ i.c.	[[_linear, ‘class A‘]]	✓

15921	$y^{'} - \frac{y}{t} = \ln (t)$	[_linear]	✓

15923	$y^{'} + y = {\begin{array}{cc} 4 & 0 \leq t < 2 \\ 0 & 2 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

15924	$y^{'} + y = {\begin{array}{cc} t & 0 \leq t < 1 \\ 0 & 1 \leq t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

15925	$y^{'} - y = \sin (2 t)$	[[_linear, ‘class A‘]]	✓

15926	$y^{'} + y = 5 e^{2 t}$	[[_linear, ‘class A‘]]	✓

15927	$y^{'} + y = e^{- t}$	[[_linear, ‘class A‘]]	✓

15928	$y^{'} + y = 2 - e^{2 t}$	[[_linear, ‘class A‘]]	✓

15929	$y^{'} - 5 y = t$	[[_linear, ‘class A‘]]	✓

15930	$y^{'} + 3 y = 27 t^{2} + 9$	[[_linear, ‘class A‘]]	✓

15931	$y^{'} - \frac{y}{2} = 5 \cos (t) + 2 e^{t}$	[[_linear, ‘class A‘]]	✓

15932	$y^{'} + 4 y = 8 \cos (4 t)$	[[_linear, ‘class A‘]]	✓

15933	$y^{'} + 10 y = 2 e^{t}$	[[_linear, ‘class A‘]]	✓

15934	$y^{'} - 3 y = 27 t^{2}$	[[_linear, ‘class A‘]]	✓

15935	$y^{'} - y = 2 e^{t}$	[[_linear, ‘class A‘]]	✓

15936	$y^{'} + y = 4 + 3 e^{t}$	[[_linear, ‘class A‘]]	✓

15937	$y^{'} + y = 2 \cos (t) + t$	[[_linear, ‘class A‘]]	✓

15938	$y^{'} + \frac{y}{2} = \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓

15939	$y^{'} - \frac{y}{2} = \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓

15940	$t y^{'} + y = t \cos (t)$	[_linear]	✓

15941	$y^{'} + y = t$ i.c.	[[_linear, ‘class A‘]]	✓

15942	$y^{'} + y = \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓

15943	$y^{'} + y = \cos (t)$ i.c.	[[_linear, ‘class A‘]]	✓

15944	$y^{'} + y = e^{t}$ i.c.	[[_linear, ‘class A‘]]	✓

15947	$y \cos (t y) + t \cos (t y) y^{'} = 0$	[_separable]	✓

15948	$y \sec {(t)}^{2} + 2 t + \tan (t) y^{'} = 0$	[_linear]	✓

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]	✓

15966	$- 2 t y^{2} \sin (t^{2}) + 2 y \cos (t^{2}) y^{'} = 0$	[_separable]	✓

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]	✓

15976	$2 t y + 3 t^{2} + (t^{2} - 1) y^{'} = 0$ 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]	✓

16016	$2 y - 3 t + t y^{'} = 0$	[_linear]	✓

16021	$t - y + t y^{'} = 0$	[_linear]	✓

16034	$t + y - t y^{'} = 0$ i.c.	[_linear]	✓

16044	$y^{'} - \frac{2 y}{x} = - x^{2} y$	[_separable]	✓

16053	$y = t (y^{'} + 1) + 2 y^{'} + 1$	[_linear]	✓

16065	$y^{'} = \frac{(4 - 7 x) (2 y - 3)}{(- 1 + x) (2 x - 5)}$	[_separable]	✓

16066	$y^{'} + 3 y = - 10 \sin (t)$	[[_linear, ‘class A‘]]	✓

16069	$y - x + y^{'} = 0$	[[_linear, ‘class A‘]]	✓

16078	$y^{'} + t y = t$	[_separable]	✓

16079	$x^{'} + \frac{x}{y} = y^{2}$	[_linear]	✓

16080	$t r^{'} + r = t \cos (t)$	[_linear]	✓

16097	$y^{'} = - \frac{y}{t - 2}$ i.c.	[_separable]	✓

16221	$y^{'} - 4 y = t^{2}$	[[_linear, ‘class A‘]]	✓

16222	$y^{'} + y = \cos (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓

16223	$y^{'} - y = e^{4 t}$ i.c.	[[_linear, ‘class A‘]]	✓

16224	$y^{'} + 4 y = e^{- 4 t}$ i.c.	[[_linear, ‘class A‘]]	✓

16225	$y^{'} + 4 y = t e^{- 4 t}$	[[_linear, ‘class A‘]]	✓

16596	$x y^{'} + y = \cos (x)$	[_linear]	✓

16597	$2 y + y^{'} = e^{x}$	[[_linear, ‘class A‘]]	✓

16598	$(- x^{2} + 1) y^{'} + x y = 2 x$	[_separable]	✓

16600	$y^{'} = x + y$	[[_linear, ‘class A‘]]	✓

16601	$y^{'} = y - x$	[[_linear, ‘class A‘]]	✓

16602	$y^{'} = \frac{x}{2} - y + \frac{3}{2}$	[[_linear, ‘class A‘]]	✓

16604	$y^{'} = (y - 1) x$	[_separable]	✓

16607	$y^{'} = y - x^{2}$	[[_linear, ‘class A‘]]	✓

16608	$y^{'} = x^{2} + 2 x - y$	[[_linear, ‘class A‘]]	✓

16609	$y^{'} = \frac{y + 1}{- 1 + x}$	[_separable]	✓

16612	$y^{'} = 2 x - y$	[[_linear, ‘class A‘]]	✓

16613	$y^{'} = x^{2} + y$	[[_linear, ‘class A‘]]	✓

16614	$y^{'} = - \frac{y}{x}$	[_separable]	✓

16621	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓

16622	$y^{'} = 2 y - 2 x^{2} - 3$ i.c.	[[_linear, ‘class A‘]]	✓

16623	$x y^{'} = 2 x - y$ i.c.	[_linear]	✓

16626	$\sin (x) y^{'} - y \cos (x) = 0$ i.c.	[_separable]	✓

16638	$y^{'} = a x + b y + c$	[[_linear, ‘class A‘]]	✓

16640	$x y^{'} + y = a (1 + x y)$ i.c.	[_linear]	✓

16642	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓

16655	$(x + 1) y^{'} = y - 1$	[_separable]	✓

16656	$y^{'} = 2 x (π + y)$	[_separable]	✓

16659	$x - y + x y^{'} = 0$	[_linear]	✓

16666	$x + y - 2 + (1 - x) y^{'} = 0$	[_linear]	✓

16678	$2 y + y^{'} = e^{- x}$	[[_linear, ‘class A‘]]	✓

16679	$x^{2} - x y^{'} = y$ i.c.	[_linear]	✓

16680	$y^{'} - 2 x y = 2 x e^{x^{2}}$	[_linear]	✓

16681	$y^{'} + 2 x y = e^{- x^{2}}$	[_linear]	✓

16682	$\cos (x) y^{'} - y \sin (x) = 2 x$ i.c.	[_linear]	✓

16683	$x y^{'} - 2 y = x^{3} \cos (x)$	[_linear]	✓

16684	$y^{'} - y \tan (x) = \frac{1}{\cos {(x)}^{3}}$ i.c.	[_linear]	✓

16685	$x \ln (x) y^{'} - y = 3 x^{3} \ln {(x)}^{2}$	[_linear]	✓

16687	$y^{'} + y \cos (x) = \cos (x)$ i.c.	[_separable]	✓

16690	$y^{'} - y e^{x} = 2 x e^{e^{x}}$	[_linear]	✓

16691	$y^{'} + x e^{x} y = e^{(1 - x) e^{x}}$	[_linear]	✓

16692	$y^{'} - y \ln (2) = 2^{\sin (x)} (\cos (x) - 1) \ln (2)$	[[_linear, ‘class A‘]]	✓

16693	$y^{'} - y = - 2 e^{- x}$ i.c.	[[_linear, ‘class A‘]]	✓

16694	$\sin (x) y^{'} - y \cos (x) = - \frac{\sin {(x)}^{2}}{x^{2}}$ i.c.	[_linear]	✓

16695	$x^{2} y^{'} \cos (\frac{1}{x}) - y \sin (\frac{1}{x}) = - 1$ i.c.	[_linear]	✓

16696	$2 x y^{'} - y = 1 - \frac{2}{\sqrt{x}}$ i.c.	[_linear]	✓

16697	$x^{2} y^{'} + y = (x^{2} + 1) e^{x}$ i.c.	[_linear]	✓

16698	$x y^{'} + y = 2 x$	[_linear]	✓

16699	$\sin (x) y^{'} + y \cos (x) = 1$	[_linear]	✓

16700	$\cos (x) y^{'} - y \sin (x) = - \sin (2 x)$ i.c.	[_linear]	✓

16704	$y^{'} + 3 x y = y e^{x^{2}}$	[_separable]	✓

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]	✓

16729	$x^{2} + y - x y^{'} = 0$	[_linear]	✓

16731	$2 x^{2} y + 2 y + 5 + (2 x^{3} + 2 x) y^{'} = 0$	[_linear]	✓

16739	${y^{'}}^{2} - 2 y y^{'} = y^{2} (e^{2 x} - 1)$	[_separable]	✓

16742	${y^{'}}^{2} - (2 x + y) y^{'} + x^{2} + x y = 0$	[_quadrature]	✓

16789	$x \sin (x) y^{'} + (\sin (x) - x \cos (x)) y = \sin (x) \cos (x) - x$	[_linear]	✓

16795	$2 x y e^{x^{2}} - x \sin (x) + e^{x^{2}} y^{'} = 0$	[_linear]	✓

16800	$(2 x - 1) y^{'} - 2 y = \frac{1 - 4 x}{x^{2}}$	[_linear]	✓

16803	$y^{'} (3 x^{2} - 2 x) - y (6 x - 2) = 0$	[_separable]	✓

17244	$x^{2} y^{'} = y - x y$ i.c.	[_separable]	✓

17258	$y^{'} + 4 y = t + e^{- 2 t}$	[[_linear, ‘class A‘]]	✓

17259	$y^{'} - 2 y = t^{2} e^{2 t}$	[[_linear, ‘class A‘]]	✓

17260	$y^{'} + y = t e^{- t} + 1$	[[_linear, ‘class A‘]]	✓

17261	$y^{'} + \frac{y}{t} = 5 + \cos (2 t)$	[_linear]	✓

17262	$y^{'} - 2 y = 3 e^{t}$	[[_linear, ‘class A‘]]	✓

17263	$t y^{'} + 2 y = \sin (t)$	[_linear]	✓

17264	$y^{'} + 2 t y = 16 t e^{- t^{2}}$	[_linear]	✓

17265	$(t^{2} + 1) y^{'} + 4 t y = \frac{1}{{(t^{2} + 1)}^{2}}$	[_linear]	✓

17266	$y + 2 y^{'} = 3 t$	[[_linear, ‘class A‘]]	✓

17267	$t y^{'} - y = t^{3} e^{- t}$	[_linear]	✓

17268	$y^{'} + y = 5 \sin (2 t)$	[[_linear, ‘class A‘]]	✓

17269	$y + 2 y^{'} = 3 t^{2}$	[[_linear, ‘class A‘]]	✓

17270	$y^{'} - y = 2 t e^{2 t}$ i.c.	[[_linear, ‘class A‘]]	✓

17271	$y^{'} + 2 y = t e^{- 2 t}$ i.c.	[[_linear, ‘class A‘]]	✓

17272	$t y^{'} + 4 y = t^{2} - t + 1$ i.c.	[_linear]	✓

17273	$y^{'} + \frac{2 y}{t} = \frac{\cos (t)}{t^{2}}$ i.c.	[_linear]	✓

17274	$y^{'} - 2 y = e^{2 t}$ i.c.	[[_linear, ‘class A‘]]	✓

17275	$t y^{'} + 2 y = \sin (t)$ i.c.	[_linear]	✓

17276	$t^{3} y^{'} + 4 t^{2} y = e^{- t}$ i.c.	[_linear]	✓

17277	$t y^{'} + (t + 1) y = t$ i.c.	[_linear]	✓

17278	$y^{'} - \frac{y}{3} = 3 \cos (t)$ i.c.	[[_linear, ‘class A‘]]	✓

17279	$2 y^{'} - y = e^{\frac{t}{3}}$ i.c.	[[_linear, ‘class A‘]]	✓

17280	$3 y^{'} - 2 y = e^{- \frac{π t}{2}}$ i.c.	[[_linear, ‘class A‘]]	✓

17281	$t y^{'} + (t + 1) y = 2 t e^{- t}$ i.c.	[_linear]	✓

17282	$t y^{'} + 2 y = \frac{\sin (t)}{t}$ i.c.	[_linear]	✓

17283	$\sin (t) y^{'} + y \cos (t) = e^{t}$ i.c.	[_linear]	✓

17284	$y^{'} + \frac{y}{2} = 2 \cos (t)$ i.c.	[[_linear, ‘class A‘]]	✓

17285	$y^{'} + \frac{4 y}{3} = 1 - \frac{t}{4}$ i.c.	[[_linear, ‘class A‘]]	✓

17286	$y^{'} + \frac{y}{4} = 3 + 2 \cos (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓

17287	$y^{'} - y = 1 + 3 \sin (t)$ i.c.	[[_linear, ‘class A‘]]	✓

17288	$y^{'} - \frac{3 y}{2} = 3 t + 3 e^{t}$ i.c.	[[_linear, ‘class A‘]]	✓

17289	$y^{'} - 6 y = t^{6} e^{6 t}$	[[_linear, ‘class A‘]]	✓

17290	$y^{'} + \frac{y}{t} = 3 \cos (2 t)$	[_linear]	✓

17291	$t y^{'} + 2 y = \sin (t)$	[_linear]	✓

17292	$y + 2 y^{'} = 3 t^{2}$	[[_linear, ‘class A‘]]	✓

17293	$(t - 3) y^{'} + \ln (t) y = 2 t$ i.c.	[_linear]	✓

17294	$t (- 4 + t) y^{'} + y = 0$ i.c.	[_separable]	✓

17295	$y^{'} + y \tan (t) = \sin (t)$ i.c.	[_linear]	✓

17296	$(- t^{2} + 4) y^{'} + 2 t y = 3 t^{2}$ i.c.	[_linear]	✓

17297	$(- t^{2} + 4) y^{'} + 2 t y = 3 t^{2}$ i.c.	[_linear]	✓

17298	$y + \ln (t) y^{'} = \cot (t)$ i.c.	[_linear]	✓

17314	$y^{'} + 2 y = {\begin{array}{cc} 1 & 0 \leq t \leq 1 \\ 0 & 1 < t \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓

17315	$y^{'} + ({\begin{array}{cc} 2 & 0 \leq t \leq 1 \\ 1 & 1 < t \end{array}) y = 0$ i.c.	[_separable]	✓

17319	$2 x y^{2} + 2 y + (2 x + 2 x^{2} y) y^{'} = 0$	[_separable]	✓

17325	$\frac{y}{x} + 6 x + (\ln (x) - 2) y^{'} = 0$	[_linear]	✓

17335	$y^{'} = e^{2 x} + y - 1$	[[_linear, ‘class A‘]]	✓

17367	$x y^{'} + (x + 1) y = x$	[_linear]	✓

17369	$\frac{\sqrt{x} y^{'}}{y} = 1$	[_separable]	✓

17370	$5 x y^{2} + 5 y + (5 x^{2} y + 5 x) y^{'} = 0$	[_separable]	✓

17372	$(2 - x) y^{'} = y + 2 {(2 - x)}^{5}$	[_linear]	✓

17828	$\cos (x) y^{'} = y \sin (x) + \cos {(x)}^{2}$	[_linear]	✓

17829	$y^{'} = 2 x y - x^{3} + x$	[_linear]	✓

17830	$y^{'} + \frac{x y}{x^{2} + 1} = \frac{1}{x (x^{2} + 1)}$	[_linear]	✓

17844	$y^{'} = k y + f (x)$	[[_linear, ‘class A‘]]	✓

17854	$y^{'} = 2 x y - x^{3} + x$	[_linear]	✓

17859	${y^{'}}^{3} - (y^{2} + x y + x^{2}) {y^{'}}^{2} + (x^{3} y + y^{2} x^{2} + x y^{3}) y^{'} - x^{3} y^{3} = 0$	[_quadrature]	✓

17978	$x y^{'} = 2 y$	[_separable]	✓

18002	$y^{'} = 2 x y$	[_separable]	✓

18005	$y^{'} + y \tan (x) = 0$	[_separable]	✓

18006	$y^{'} - y \tan (x) = 0$	[_separable]	✓

18021	$y^{'} = 2 x y + 1$	[_linear]	✓

18031	$x y^{'} = 2 x + 3 y$	[_linear]	✓

18041	$2 x + 3 y - 1 - 4 (x + 1) y^{'} = 0$	[_linear]	✓

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]	✓

18082	$- y + x y^{'} = 2 x^{2} - 3$	[_linear]	✓

18088	$y^{'} + \frac{y}{x} = \sin (x)$	[_linear]	✓

18090	$x y^{'} - 3 y = x^{4}$	[_linear]	✓

18091	$y^{'} + y = \frac{1}{1 + e^{2 x}}$	[_linear]	✓

18092	$(x^{2} + 1) y^{'} + 2 x y = \cot (x)$	[_linear]	✓

18093	$y^{'} + y = 2 x e^{- x} + x^{2}$	[[_linear, ‘class A‘]]	✓

18094	$y^{'} + y \cot (x) = 2 x \csc (x)$	[_linear]	✓

18095	$2 y - x^{3} = x y^{'}$	[_linear]	✓

18096	$y - x + x y \cot (x) + x y^{'} = 0$	[_linear]	✓

18097	$y^{'} - 2 x y = 6 x e^{x^{2}}$	[_linear]	✓

18098	$x \ln (x) y^{'} + y = 3 x^{3}$	[_linear]	✓

18099	$y - 2 x y - x^{2} + x^{2} y^{'} = 0$	[_linear]	✓

18107	$y^{'} \sin (2 x) = 2 y + 2 \cos (x)$	[_linear]	✓

18131	$x^{2} + y = x y^{'}$	[_linear]	✓

18132	$x y^{'} + y = x^{2} \cos (x)$	[_linear]	✓

18138	$y^{'} + 2 x y = e^{- x^{2}}$	[_linear]	✓

18140	$(x^{2} + 1) y^{'} + 2 x y = 4 x^{3}$	[_linear]	✓

18146	$y^{'} = 1 + 3 y \tan (x)$	[_linear]	✓

18152	$\frac{y - x}{{(x + y)}^{3}} - \frac{2 x y^{'}}{{(x + y)}^{3}} = 0$	[_linear]	✓

18156	$x (x^{2} + 1) y^{'} + 2 y = {(x^{2} + 1)}^{3}$	[_linear]	✓

18158	$e^{x^{2} y} (1 + 2 x^{2} y) + x^{3} e^{x^{2} y} y^{'} = 0$	[_linear]	✓

18166	$x y + y - 1 + x y^{'} = 0$	[_linear]	✓

18169	$x^{'} + x \cot (y) = \sec (y)$	[_linear]	✓

18422	$1 + 2 x + (- t^{2} + 4) x^{'} = 0$	[_separable]	✓

18425	$x^{'} e^{3 t} + 3 x e^{3 t} = 2 t$	[[_linear, ‘class A‘]]	✓

18427	$x^{'} + 2 x = e^{t}$	[[_linear, ‘class A‘]]	✓

18428	$x^{'} + x \tan (t) = 0$	[_separable]	✓

18429	$x^{'} - x \tan (t) = 4 \sin (t)$	[_linear]	✓

18430	$t^{3} x^{'} + (- 3 t^{2} + 2) x = t^{3}$	[_linear]	✓

18432	$t x^{'} + x \ln (t) = t^{2}$	[_linear]	✓

18433	$t x^{'} + x g (t) = h (t)$	[_linear]	✓

18458	$v^{'} + u^{2} v = \sin (u)$	[_linear]	✓

18460	$v^{'} + \frac{2 v}{u} = 3$	[_linear]	✓

18463	$y - x y^{'} = b (1 + x^{2} y^{'})$	[_separable]	✓

18473	$y^{'} + x y = x$	[_separable]	✓

18474	$y^{'} + \frac{y}{x} = \sin (x)$	[_linear]	✓

18476	$p^{'} = \frac{p + a t^{3} - 2 p t^{2}}{t (- t^{2} + 1)}$	[_linear]	✓

18478	$y^{'} + y \cos (x) = \frac{\sin (2 x)}{2}$	[_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]	✓

18497	$v^{'} + 2 u v = 2 u$	[_separable]	✓

18509	$5 x^{'} + x = \sin (3 t)$	[[_linear, ‘class A‘]]	✓

18525	$y^{'} + \frac{x y}{x^{2} + 1} = \frac{1}{x (x^{2} + 1)}$	[_linear]	✓

18540	$y^{'} + \frac{y}{x} = - x^{2} + 1$	[_linear]	✓

18541	$y^{'} + y \cot (x) = \csc {(x)}^{2}$	[_linear]	✓

18542	$y^{'} = x - y$	[[_linear, ‘class A‘]]	✓

18544	$y^{'} + \frac{x y}{x^{2} + 1} = \frac{1}{x (x^{2} + 1)}$	[_linear]	✓

18545	$x (- x^{2} + 1) y^{'} + (x^{2} - 1) y = x^{3}$	[_linear]	✓

18546	$y^{'} + y \cos (x) = \frac{\sin (2 x)}{2}$	[_linear]	✓

18547	$x (- x^{2} + 1) y^{'} + (2 x^{2} - 1) y = a x^{3}$	[_linear]	✓

18566	$(x^{2} - 2 x y) y^{'} + x^{2} - 3 x y + 2 y^{2} = 0$	[_linear]	✓

18648	$(1 - x) y^{'} - y - 1 = 0$	[_separable]	✓

18663	$y - x y^{'} + \ln (x) = 0$	[_linear]	✓

18677	$x y^{'} - a y = x + 1$	[_linear]	✓

18678	$y^{'} + y = e^{- x}$	[[_linear, ‘class A‘]]	✓

18679	$\cos {(x)}^{2} y^{'} + y = \tan (x)$	[_linear]	✓

18680	$(x + 1) y^{'} - n y = e^{x} {(x + 1)}^{n + 1}$	[_linear]	✓

18681	$(x^{2} + 1) y^{'} + 2 x y = 4 x^{2}$	[_linear]	✓

18692	$y^{'} + \frac{(1 - 2 x) y}{x^{2}} = 1$	[_linear]	✓

18695	$y^{'} + \frac{y}{\sqrt{- x^{2} + 1}} = \frac{x + \sqrt{- x^{2} + 1}}{{(- x^{2} + 1)}^{2}}$	[_linear]	✓

18698	$y^{'} + \frac{4 x y}{x^{2} + 1} = \frac{1}{{(x^{2} + 1)}^{3}}$	[_linear]	✓

18700	$x (- x^{2} + 1) y^{'} + (2 x^{2} - 1) y = a x^{3}$	[_linear]	✓

18711	$\sqrt{a^{2} + x^{2}} y^{'} + y = \sqrt{a^{2} + x^{2}} - x$	[_linear]	✓

18715	$y - x y^{'} = b (1 + x^{2} y^{'})$	[_separable]	✓

18720	$y^{'} + \frac{n y}{x} = a x^{- n}$	[_linear]	✓

18757	${y^{'}}^{2} + 2 y y^{'} \cot (x) = y^{2}$	[_separable]	✓

18762	${y^{'}}^{3} - (y^{2} + x y + x^{2}) {y^{'}}^{2} + (x^{3} y + y^{2} x^{2} + x y^{3}) y^{'} - x^{3} y^{3} = 0$	[_quadrature]	✓

18968	$y + x + x y^{'} = 0$	[_linear]	✓

18975	$(- x^{2} + 1) y^{'} - 2 x y = - x^{3} + x$	[_linear]	✓

18976	$x y^{'} - y - \cos (\frac{1}{x}) = 0$	[_linear]	✓

18980	$x^{2} y^{'} + y = 1$	[_separable]	✓

18981	$2 y + (x^{2} + 1) \arctan (x) y^{'} = 0$	[_separable]	✓

19017	$y^{'} + y \cot (x) = 2 \cos (x)$	[_linear]	✓

19018	$\cos {(x)}^{2} y^{'} + y = \tan (x)$	[_linear]	✓

19019	$x \cos (x) y^{'} + y (x \sin (x) + \cos (x)) = 1$	[_linear]	✓

19020	$y - x \sin (x^{2}) + x y^{'} = 0$	[_linear]	✓

19021	$x \ln (x) y^{'} + y = 2 \ln (x)$	[_linear]	✓

19022	$\sin (x) \cos (x) y^{'} = y + \sin (x)$	[_linear]	✓

19025	$y^{'} + 3 x^{2} y = x^{5} e^{x^{3}}$	[_linear]	✓

19027	$y^{'} + \frac{(1 - 2 x) y}{x^{2}} = 1$	[_linear]	✓

19028	$y^{'} + \frac{2 y}{x} = \sin (x)$	[_linear]	✓

19030	$1 + y + x^{2} y + (x^{3} + x) y^{'} = 0$	[_linear]	✓

19031	$y^{'} + \frac{x y}{x^{2} + 1} = \frac{1}{2 x (x^{2} + 1)}$	[_linear]	✓

19076	$y^{'} + \frac{y}{{(- x^{2} + 1)}^{3 / 2}} = \frac{x + \sqrt{- x^{2} + 1}}{{(- x^{2} + 1)}^{2}}$	[_linear]	✓

19136	${y^{'}}^{2} + 2 y y^{'} \cot (x) = y^{2}$	[_separable]	✓

19138	$y^{'} (y^{'} - y) = (x + y) x$	[_quadrature]	✓

19141	$x {y^{'}}^{2} + (y - x) y^{'} - y = 0$	[_quadrature]	✓

19144	${y^{'}}^{3} - y^{'} (y^{2} + x y + x^{2}) + x y (x + y) = 0$	[_quadrature]	✓

19145	$(y^{'} + y + x) (y + x + x y^{'}) (y^{'} + 2 x) = 0$	[_quadrature]	✓

19158	$y = \sin (x) y^{'} + \cos (x)$	[_linear]	✓

19231	$4 {y^{'}}^{2} x^{2} (- 1 + x) - 4 y^{'} x y (4 x - 3) + (16 x - 9) y^{2} = 0$	[_separable]	✓

19234	$y - x y^{'} = b (1 + x^{2} y^{'})$	[_separable]	✓

19430	$y - x y^{'} = 0$	[_separable]	✓

19439	$\cos (x) y^{'} + y \sin (x) = 1$	[_linear]	✓

19440	$y^{'} + 2 x y = e^{- x^{2}}$	[_linear]	✓

19465	${y^{'}}^{3} - (y^{2} + x y + x^{2}) {y^{'}}^{2} + (x^{3} y + y^{2} x^{2} + x y^{3}) y^{'} - x^{3} y^{3} = 0$	[_quadrature]	✓

2.3.1 ﬁrst order ode linear